Friday, 5 November 2010

On Omniscience and Freewill

Despite my blog exposing the logical fallacy of an inerrantly omniscient god and free will, it seems the full implications of this have gone unnoticed by many.

Let’s recap:

We are discussing the god of the Bible which Christians, Jews and Moslem all regard as omniscient (all-knowing) and whom they believe has granted mankind free will.

Following from this is the idea that, by exercising this free will, mankind committed the ultimate sin of disobeying God and must now seek God’s forgiveness. God does not pre-ordain our decisions so we bear sole responsibility for our own actions and are accountable to God for them. At the same time, God is all knowing and inerrant and so knows everything with absolute certainty. He knows everything about the past, present and future and is never wrong, ever.

Christians, Jews and Muslims and their various sects all believe they alone know the special secrets for gaining this god’s forgiveness for this supposed supreme sin of disobeying God. The only way to achieve this is by joining them, accepting their dogmas and following their rituals.

Furthermore, mankind knows about this sin, about God’s inerrant omniscience, about mankind’s free will and about the need for forgiveness, because it’s all written down in a book either written by, dictated by or inspired by this inerrant (and perfect) god, so it too is inerrant and absolutely true.

Surprisingly though, a simple question which can be answered with a simple “yes” or “no” answer seems to put Christians, Jews and Muslims all into the same flat panic.

The simple question is:

If God has always known what you will have for breakfast tomorrow, can you choose to have something else instead?

So what exactly is the problem here?

Let’s consider the possible answers:

Answer 1. Yes.

Ah! Then something can happen that God didn’t know about, so God is not omniscient or inerrant. God got it wrong, and god didn’t know your eventual choice.

And the Bible is wrong about the god described in it.

Oops!

Answer 2. No.

Ah! So you can't chose to do something other than what God has known you’ll do, and had known for ever that you’ll do, even from before he (so it is believe) created you.

In that case, God’s inerrant omniscience means you don't have free will and your actions have all been pre-determined for you by God’s prior knowledge of your actions. In effect, you are no different to an automaton.

And, as a mere automaton of course, you can’t be held responsible for you actions. Accountability lies with the person controlling you – which is er... God.

And that means all this stuff about human disobedience, sin and needing to beg God for forgiveness is wrong.

Oops!

So how to resolve this paradox?

Well, we could always argue that this God isn’t actually inerrantly omniscient. That restores human free will and our accountability for our own actions, but where does it leave God?

It leaves God as someone who is less than perfect, who makes mistakes and doesn’t actually know everything. In fact, it makes God unfit to judge us humans and condemn us for making mistakes, being less than perfect and not knowing everything. In fact, it places God on an equal footing to humans.

Perhaps there are Christians, Muslims and Jews who can accept that, but where does it leave the Bible?

The Bible is no longer the inerrant word of an omniscient god. In fact it’s wrong on at least one, if not both, the central tenets of Christianity, Judaism and Islam. It’s either wrong about the nature of God, or about human free will, or both. Moreover, the moral judgement of the god described in it is now in question. This god has apparently judged humans to be sinful when it is also capable of doing wrong. Let him who is without guilt cast the first stone.

The Bible is no more reliable as a guide to truth and morality than had it been written by mere humans, (which of course is precisely who wrote it and why it can be safely dismissed as a guide to truth and morality).

Clearly there is no satisfactory way to resolve this problem.

And the entire foundation of three major world religions has just collapsed under its own internal contradiction. The thread upon which the whole edifice dangled has just vanished, if you'll excuse a slightly mixed metaphor.

And, when you ask a Christian, Jew or Moslem that simple little question, requiring a simple yes or no answer, you will quickly discover that either they have never thought about the central tenets of their ‘faith’, or they are only too well aware of the lie at the heart of it. They will either blunder into an answer, and then squirm as you point out the implication of it, or, much more likely, they will wriggle and squirm and do anything but give an honest answer.

A very nice example of this can bee seen at Chirpstory - Christian Dishonesty where a fundamentalist Christian starts off confidently answering a question until he realises where it's leading, then nothing will induce him to give a straight yes or no answer to a simple question. Clearly he knows whichever answer he gives will expose the lie he knows exists at the very heart of his 'faith'.

These latter ones are the ones who are well aware that their professed ‘faith’ is a lie. These will usually be the ones who are actively trying to persuade others into believing something they know to be false. These will be those proudly pious people who make smugly condescending pronouncements about the shortcomings of others and about their special relationship with God and how this gives them a short-cut to knowledge which is unquestionably superior to that gained through diligent learning and reason. They may also be the priests, pastors, preachers, clerics, rabbis, imams and other snake-oil salesmen who have a vested interest in trying to control you through the fear and superstition they themselves know to be untrue.

These will be the ones claiming to know the magic spells, rituals and incantations which will help you gain this god’s forgiveness; a forgiveness they know to be unnecessary for a guilt they know to be unjustified from a god they know does not exist.

This central logical contradiction at the heart of all the Abrahamic, guilt-based religions betrays their human origins and the desire to exert control over others which motivated them.

And it takes only a simple little question to expose the many charlatans who feast off the opportunities it creates for controlling others and the many phoney pious Christians, Muslims and Jews who know their 'faith' is a lie but none-the-less continue to piously profess it because it allows them to pose as superior to the rest of us.

These morally bankrupt Atheists (for that is what they are) are a disgrace to humanity. As a fellow Atheist I am ashamed of them and their moral degeneracy. As a human being I am angry at the harm they've done to people, to human culture and to the societies they've perverted for their own nefarious purposes.

We can be better than that. For the sake of humanity we should do better than that.

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226 comments
:

God is all-knowing but does not force our hand. We still have free will and the ability to chose for ourselves who we will serve and although He knows what we will decide He allows us to make that choice, right or wrong. Free will and the omnniscience of God are not in contradiction to one another. John 3:16 For God so loved the world that He gave His only begotten son that whosoever believes in Him will not perish but have everlasting life.

You weren't able to give a simple yes or no answer to that simple question, then?

So, now we know you know your 'faith' is a lie beyond any reasonable doubt, would you care to tell us who you're hoping to fool with your preaching, and why you want to persuade them to believe something you know to be false?

Most people of "faith" consider belief in impossible things to be a net positive. They delight in it, because to them, overcoming doubts is a victory over Satan who is the one responsible for making the whole thing look impossible, sowing the seeds of doubt and disbelief.

With that type of reasoning, you can't win.

There are so many things in the bible/quran/torah which are just flat out impossible. The classic is "Can God create a stone so heavy that God can't move it", which shows the basic impossibility of omnipotence, but to the true believer it isn't a disproof at all, it is just something to ponder to "bring him closer to God". Mankind has wasted thousands of years thinking about such things.

It is a strange reality that often atheists are more theologically educated than many theists. Likewise, it is amazing how many theists fall right into line with straw-man stereotypes of theistic ways of thinking.

I must take issue, though, with your conclusions in this article not because there are Christian and Muslim theists in abundance who actually exhibit variegates of your characterizations above but because there are other perspectives that escape this omniscience-free will-and theodicy trap.

Note: I am not a theist. I am somewhere between atheism and transtheism but a thorough humanist and skeptic. However, as stated, there are other theistic models aside from the strict predestination-model of divine sovereignty.

For example, open theism posits a God with limited knowledge of the future (a limitation that is either of God's volition or ontologically related to what can be known). In this model humans have complete free will and can do and behave in ways that might surprise even God. In open theistic models, God might be said to know all possibilities in advance but not to know the actual events until they transpire.

It is worth noting that most open theists are Evangelicals and believe in a inerrant Bible. That is, they have developed theological hermeneutics that do not confine their exegetical endeavors to strict predestination and foreknowledge. Frankly, I find their exegetical assumptions to be far more congruent with sound historical-critical hermeneutics than the post-Augustinian and hellenistic assumptions of classical theism.

Another model which is far less concerned with the Bible is process theism, but I will stop for now at this.

Classical theism is stuck in Hellenistic/Greek ways of thinking that make it incumbent on all-powerful creator to know all and be transcendentally all powerful. In the Hebrew Bible the deity is far more mundane--often expressing surprise and limited knowledge in the face of human affairs. Later Jews and Christians now call these biblical events literary devises or anthropomorphism, but it is far from likely that the original Hebrew readers of these texts would have seen them as such.

There are several models of open theism and process theology, but all posit limited knowledge of the future on the part of the deity. There is too much stuff to say on this...so I'll leave it here. But, I just want to illustrate that their are theistic permutations that leap the hurdle of classically-defined omniscience and free will.

The simple answer to your dilemma is "Yes." But the consequence you draw -- that "God got it wrong" -- does not follow. It would follow if your question had been a slightly different one: "... will you choose to have something else instead?" The proper answer to that question would be "No."

There is a substantial literature on modality, choice, and omniscience. It might be a good idea to have a look at it before assuming that everyone who maintains the compatibility of omniscience and free will is a charlatan who can be exposed by a simple question like this.

Er... no. It follows from that answer that God can be wrong; that you CAN do something God didn't know you would do.

I'm familar with the usual standards of theology in which the outcome is pre-determined then the 'logic' is built around the desired answer with any amount of bending permitted until the right conclusion is reached.

Theology, in other words, is a carefully constructed workaround or a skilled avoidance of the obstacles with which religion needs to cope.

"Er... no. It follows from that answer that God can be wrong; that you CAN do something God didn't know you would do."

Sorry, but actually, it does not follow. You will do X. God knows (and has known) that you will do X. You are free to do Y instead of X. But if you were to do Y, then it would have been the case all along that God knew that you would do Y. No contradiction emerges at any point.

You can complain, if you like, about omniscience; you can argue that no being could have that kind of knowledge. But you cannot generate a contradiction from the mere combination of freedom and foreknowledge.

In fact, it's important that you not be able to, since otherwise anyone's knowledge of the past would render people's actions unfree by parallel reasoning. "I know that, in point of fact, he took the train. Could he have taken the bus instead?" etc. The argument works in both cases or in neither. In this case, it's neither.

Just found this blog after linking to it from apologetics 315. I like how you are thoughtfully considering these issues. It's sad that more of my fellow Christians don't think about these things. However, I disagree.

Tim is 100% correct. This assumption that somehow free will and omniscience are in conflict is based on a fundamental modal fallacy.

But this reasoning is fallacious. All that would actually follow from the premises displayed is Q. In terms of God's foreknowledge, all that would follow is that x will happen, not that necessarily x will happen.

That means that something other than X COULD have happened. But as Tim rightly says, if something other than X will have happened due to some free choice, then God would have known that.

In other words, God knows the free choice itself. That doesn't have any bearing on what free choice is made.

No. The question was as I stated it. What you and Tim are doing is not answering it and adopting the coping strategy of complaining I should have asked a different one, then weaving an ellaborate rationalisation for so doing.

It's a simple question, requiring a simple yes or no answer, concerning what we could or couldn't do (not will or won't do) in the hypothetical presence of an inerrantly omniscient god.

Can you choose something other than what an inerrantly omniscient god has always known you choose (and the god still remain inerrantly omniscient)? Yes or No?

I am sorry that you felt moved to remove my post; the part to which you objected was merely a request for you to temper your language, and it was, I think, more moderately phrased than your own. Nevertheless, as this is your blog, I will simply repost the key content:

You write:

"I note that neither you nor Tim answered the question... "

The first line of my first post, timestamped 14 November 2010 18:57, reads:

No. It's not giving a straight answer to appear to answer it but immediately disclaim the answer by complaining that I hadn't asked that right question, with the implication that your answer was for that question instead.

You have, as I said, merely demonstrated your attempt to rationalize your avoidance of something you know to be untennable - the holding of two mutually exclusive opinions simultaneously.

The fact that you know you need to do that betrays the fact that you know that your 'faith' hangs on a non-extent thread.

If God has always known what you will have for breakfast tomorrow, can you choose to have something else instead?

And I answered the question straightforwardly: Yes.

There is nothing evasive about this.

The problem arises when you try to draw a conclusion from this answer:

Then something CAN happen that God didn’t know about, so God is not omniscient or inerrant. God got it wrong, and god didn’t know your eventual choice.

This conclusion, as both bossmanham and I have pointed out, does not follow from an affirmative answer to your question as you phrased it. The illusion to the contrary depends on a scope error in modal logic, confusing the necessity of the consequence,

□ (P -> Q),

with the necessity of the consequent,

(P -> □Q)

Now you write:

It's not giving a straight answer to appear to answer it but immediately disclaim the answer by complaining that I hadn't asked that right question, with the implication that your answer was for that question instead.

You are mistaken. My answer was for your question as you asked it. What I went on to point out is that only an affirmative answer to a different question would have the consequence you drew -- but that, to that different question, the proper answer would be "No."

You have quite reasonably requested that we deal with the subject of the discussion in a polite manner. You have now in this thread accused me of adopting "a coping strategy," weaving "an ellaborate [sic] rationalisation," and acting in bad faith. For clarification only: Are these examples of polite discussion that we are free to emulate if we believe that you have acted similarly, or would the use of such language by us toward you result in the deletion of our posts?

You seem to be having difficulty seeing this when it is stated in ordinary language, so here's the technical version. In the standard semantics for modal logic, one indexes propositions in terms of possible worlds. Here's a simple model-theoretic argument, using the standard modal system S5, to show the consistency of omniscience with freedom.

Let P = Tim will eat (only) a pop-tart for breakfast;

Let T = Tim will eat (only) toast for breakfast;

Let G(X) = God knows that X;

Let ◊X = It is possible that X.

Now, in w1, the actual world:

PG(P)~T◊T

This is a consistent set. Any contingent claim like T is possible even in a world in which it is false.

In virtue of the fact that T is possible in w1, there is some world accessible to w1 -- call it w2 -- in which T is actually true. But that world need not be w1. And there is absolutely no constraint that would license the inference from the fact that G(P) is true in w1 to the conclusion that G(P) is true in any world other than w1. The only constraint imposed by omniscience is that, in any given world, if a proposition is true, then, in that world, God knows that proposition; whereas if, in that world, a proposition is false, then, in that world, God does not believe that proposition. Since P is true in w1, G(P) is true in w1. Since P is false in w2, G(P) is false in w2.

Tim. If you do something OTHER than what God KNEW you would do then God can't be inerrant and if God didn't know what you were going to do, God can't be omniscient. No heap of verbiage can hide that simple logic. If you think you've come up with a logical construct which does then your construct is wrong.

Well, I suppose if you're determined to believe there are things God can be wrong about and yet he is still inerrant; and there are things he doesn't know yet he is still omnicient; and if you imagine you have devised a 'logic' which 'proves' that, there is probably little point in continuing this discussion. We obviously have different standard of logic. I don't use 'theologic'.

Nobody here is using "theologic." Modal logic is a major subfield of logic with a large literature -- and no, it was not invented by wild-eyed fundamentalists in order to safeguard their beliefs. You might want to have a look at standard texts like Hughes and Cresswell or Garson.

The key point you are missing is that God's foreknowledge is contingent on what you will, in fact, freely choose to do. It isn't a prediction or an educated guess. As I said right at the outset, you may wish to challenge the idea that there could be a being with knowledge like that. But this would be a very different discussion.

Your description of our position -- "there are things God can be wrong about and yet he is still inerrant" -- shows that you are still in the grip of your original error. Nobody in this conversation is maintaining that God can be both wrong and right about the same thing in the same sense at the same time. It doesn't further discourse about these topics when you repeatedly fail to understand what it is that your dialectical sparring partners are saying.

The trouble is that you haven't established any such thing: you just keep reasserting dialectical victory without engaging with what bossmanham and I are saying. Simply calling our responses a "tangled heap of verbiage" doesn't make it so. I can't see that you have made any effort in this entire discussion to understand the position that you are critiquing.

In this world, now, there is something you're going to eat for breakfast tomorrow. You and I may not be sure, now, what it is. But if I say now, "Rosa is going to eat an egg for breakfast tomorrow," and you are, in fact, going to eat that egg, then I am speaking truly now. For the sake of the argument, let’s suppose that this is, in fact, what you are going to eat. Call this the principle of future facts, FF for short.

If you are, in the libertarian sense, free either to eat the egg or not to eat the egg tomorrow, then you have a genuine choice: you can choose not to eat the egg. This is logically possible and causally possible: there is no inherent contradiction in saying that you will not eat an egg for breakfast tomorrow, and it does not violate the causal conditions already in place; you are not constrained to eat that egg. Call this the principle of free choice, FC for short.

Suppose you don’t.

That supposition is an invitation to consider a world that is a bit different from our own. For in our world, as we stipulated at the beginning, you are, in fact, going to eat that egg for breakfast tomorrow. But since your not eating the egg tomorrow is logically possible, we can contemplate the alternative. In that world, if I say, now, “Rosa is going to eat an egg for breafast tomorrow,” then I am speaking falsely now.

There is an old argument for fatalism that takes FF and FC as its starting points, the intention being to argue against FC by reductio ad absurdum. “For,” so runs this argument, “if you were to do something other than what you in fact do, then it is both true (by FF) that you eat an egg for breakfast tomorrow and false (because you don’t) that you eat an egg for breakfast. But this is impossible. Therefore, FC is false—you do not actually have free will.”

This is a defective argument. There is no actual contradiction and, therefore, no ground for the reductio.

But the defect in this argument for fatalism is essentially the same as the defect in your argument against the compatibility of foreknowledge and freedom.

The problem lies in a misunderstanding of FF. The principle does not say that if it is true now that Rosa will eat an egg for breakfast tomorrow, then this is true now whether Rosa eats that egg or not. The present truth value of that claim is contingent on what Rosa chooses to do tomorrow. If, tomorrow, Rosa chooses to eat that egg, then it is true today that Rosa will eat that egg tomorrow. If, tomorrow, Rosa chooses not to eat that egg, then it is true today that Rosa will not eat that egg tomorrow.

Once we clear this up about FF, there is no contradiction. To put it in the language of worlds, in a world where, tomorrow, Rosa chooses to eat the egg, it is true now that Rosa will eat the egg tomorrow; in a world where, tomorrow, Rosa chooses not to eat the egg, it is true now that Rosa won’t. But a contradiction would arise only if there were a conflict between what is true now—including that future tense statement about what Rosa will do—and what Rosa does tomorrow. In neither world does such a conflict arise. This is why the argument for fatalism fails.

The parallel problem with your argument should now be clear. What God knows about your future actions is contingent on what you choose to do tomorrow. God’s beliefs are not guesses, even educated guesses: God sees the future as it will in fact be. Among other things, therefore, God sees your breakfast tomorrow and knows, directly, what you choose to eat. If you are going to choose that egg, God knows now that this is going to be your choice. If you are going to choose not to have the egg, God knows now that you will decide against it. In neither case does God know something false.

So basically then, cutting through the virbiage, your argument is that, if I had asked a different question, you could have given the answer you like and so show that black CAN be white when you need it to be, therefore I must have asked the wrong question.

No, that isn't my position at all. It appears that you're ignoring what I've actually written and assuming that your initial, mistaken impression must be right.

Once more, for the record: I did answer the question you asked -- in the very first line of my first post on this thread. The answer is "Yes."

But as I have now explained several times, it doesn't entail what you think it does -- and a good thing, since if it did, then a parallel line of reasoning would eliminate free will without any need to bring in the existence of an omniscient deity.

Except, of course, that free will is ONLY eliminated in the presence of an inerrant, omniscient deity, because it's that presence which eliminates it by inevitable pre-ordaining everything by it's inerrant, omniscient nature.

But it's not; the assumption to the contrary amounts to the assumption that you have presented a sound argument for this conclusion. And that is the very point in dispute. So your reiteration of this claim is simply begging the question.

Tim. Since it's very clear now that you are unable or unwilling to believe that the conclusion of your 'logic' can possibly be anything other than the one you require, there really seems little point in continuing this conversation. I'll leave you with your evidently unshakeable belief in your ability to change the facts at will to suit your requirements.

I'm sorry that you are unwilling to engage with substantive criticism of your argument. It is somewhat frustrating to write long, irenic posts answering your initial question and explaining why your conclusion does not follow, only to have those explanations ignored as "verbiage" and to be falsely and repeatedly accused of not having answered your question. As you say, readers will be able to judge for themselves the merits of our respective positions.

As I noted earlier, there is a substantial literature on the logical analysis of foreknowledge and free will as well as related puzzles regarding the truth values of future tense contingent claims. If you ever want to find out what thoughtful theists (and even thoughtful atheists) think about these topics, it's there and waiting to be explored. I would recommend:

In addition to what you've talked about, the notion of free will as a stand alone concept is problematic. All decisions are made by our brains. Our brains are physical in nature and are governed by the laws of physics.

So two choices. If quantum effects play no role in our brain, then its future state is a function of the previous state. We may not be able to predict it, but it's set nonetheless. It's a "mindless" system so to speak.

If quantum effects DO play a role, then an element of randomness is introduced which again is beyond the scope of "free will" since "free" implies deliberation and not a randomness.

I loved this blog. Points made are completely valid. question: if God creates a someone, knowing that he'll murder someone some day, isnt that more like setting a train on a set of tracks? The tracks defined by God himself when he chose to create you. If God didnt want you to murder that person, could he not just have chosen NOT to create you? What about the murdered person? Doesnt creating someone you know will be murdered by someone else evil? free will and an omniscient God are mutually exclusive.

For me, existence itself (assuming an omniscient God exists) is a statement of intent by God. If you say God is omniscient, but allows you to do what you will, that chain of thought is nullified by creation itself, because God can choose to create you in a different way, where you wont make the same choices. So the choices you make now, are the ones God prefers you make. Free will? i dont think so.

I don't see this as the simple yes or no question you make it out to be. I see a trick question that attempts to create a logical contradiction by asking God to "know" and "not know" at the same time. The question is nonsense, and C. S. Lewis rightly pointed out, that nonsense doesn’t acquire sense and meaning simply by attaching God to it.

Expecting simple yes or no answers to questions that don't have one is not fair. How about this simple yes or no question. Do you still beat your spouse?

I'm sorry you don't see it as a simple yes or no question when it very clearly is. I'm at a loss to know how to explain that a question which asks if you can do something can be answered with a simple yes or no if you are unable to see that that is so.

Perhaps you could point out where the false assumption is which would make it a 'Do you still beat your wife?' type of question, please.

Perhaps you are assuming that the 'if God knows' clause is a false assumption. If so, then you have no need to try to rationalise the rest of the question away to avoid answering it.

No. It is NOT a simple yes or no question, which was the point of the "Do you still beat your spouse question?" type question. You can't answer yes or no, unless you actually beat your spouse, but that's not the point. I'm making the assumption that you don't.

The question can't be answered with a simple yes or not, because it sets up a paradox, one that actually has a name (Omnipotence Paradox).

See:http://skepticwiki.org/index.php/Omnipotence_Paradox

and:http://en.wikipedia.org/wiki/Omnipotence_paradox

Finally, failure to answer a "simple yes or no" question does not constitute proof of anything. It only proves that the correct answer isn't known.

Perhaps it escaped you but I didn't actually ask if you were still beating your wife. I asked if you could choose something else for breakfast. That, self-evidently, can be answered with a simple yes or no; either you CAN choose something else, or you can't.

The fact that you're performing these intellectual summersaults to avoid answering it shows me that you know you must avoid answering it at all costs, even at the cost of your own intellectual integrity.

One: If God has always known what you will have for breakfast tomorrow,This is referring to a final decision you are going to make at a specific point in time. When that specific point in time (breakfast tomorrow) arrives, you will make a final decision (what you will have). Once you start filling your face with oatmeal, toast, Wheaties, whatever, and finish, you've made your final decision (what you had). If God has always known your final decision, then, God has always known what you will have for breakfast tomorrow.

Two: can you choose to have something else?Prior to breakfast tomorrow, you can change your mind a million times. Once you reach that specific point in time (breakfast tomorrow), and make your decision (what you will have), you won't be able to change your mind anymore. "What you will have" will become "What you are having," which leads to "what you had." At some point during that process you made a final decision about what you will have for breakfast, and had it.

You can't go back in time, therefore, you can't choose to have something else.

Second: Conclusion Against Free WillThe question itself is misleading, because by placing God's knowledge into it, it creates the idea that God is responsible for your ability to choose or not choose. As I pointed out, this is false. In addition to that, the term "known" is ambiguous. If we rephrase the question, and clarify "known" we get:

Q1. If God has always known (predetermined by Him) what you will have for breakfast tomorrow, do you have free will?A1. No. If God had established or decided in advance your final decision, and you had no choice in the matter, then you DO NOT have free will.

Q2. If God has always known (foreknowledge of your choice) what you will have for breakfast tomorrow, do you have free will?A2. Yes. Even though God had awareness of your final decision before it was made, as long as your final decision was yours, you DO have free will.

So, to summarize:Q. If God has always known what you will have for breakfast tomorrow, can you choose to have something else?A. No, because you can't go back in time. God's knowing in advance is irrelevant to the question.

As I've already shown, the consequence you want to draw does not follow from the premises. And a good thing too, or else it would follow simply from the fact that future-tense statements about your free actions have truth values now. Fortunately (for human freedom), the inference is simply invalid.

I have spelled this out using modal logic, I have explained it verbally, and I have given you a guide to the extensive literature discussing this subject.

If you are interested in pursuing this at a level beyond merely repeating what you started with, do let us all know.

Tim. No. What you've shown is that, if you are inventive enough and prepared to abandon any pretense of personal integrity, you can find a workaround for this problem that you can convince yourself deals with it.

I think most intellectually honest people would prefer not to have to go to those lenghths just to retain an infantile self-delusion.

I'm sorry you're not up for the critical examination of your own ideas. It's something that both theists and atheists would do well to cultivate. But representatives of both sides of the debate seem to prefer to stand pat and repeat their talking points instead of engaging in the give-and-take of argument.

Are you going to explain why you needed to pretend I had asked a different question rather than answering the one I actually asked? Only if you explain why you need to pretend I didn't answer it.

Since you know the difference between predetermined and foreknowledge, then would you agree with both of the following statements?

- If someone has predetermined your actions, they have made your choices. You lose the ability to choose for yourself.- If someone has foreknowledge of your actions, they know of your choices. You retain the ability to choose for yourself.

The fact that you're performing these intellectual diversions in order to avoid answering my question "shows me that you know you must avoid answering it at all costs, even at the cost of your own intellectual integrity."

You're still pretending not to have read my answer, just as you're pretending to have answered my original question.

The great thing is that you're doing EXACTLY what I predicted you would do, knowing, as you undoubtedly do, that there is a lie at the heart of your 'faith' which you must avoid confronting at all costs in order to maintain your delusion.

The only possible explanation for this bizarre behaviour is an irrational phobia. The technical term for this particular one is theophobia.

No doubt you would proudly describe yourself as 'godfearing' without the slightest sense of irony.

Prediction is inference regarding future states of a syatem based on prior and present states of the system. Foreknowledge need not be predictive: it can be direct knowledge, not inference. You don't take account of this possibility; therefore, what you are criticising isn't the position that your opponents actually hold. They don't believe that God's knowledge about what will happen in the future is a guess, even an informed guess.

There is a literature on this issue; you might want to have a look before you make any further comments on it, since it doesn't advance the discussion much if you do not know what your opponents are actually claiming. See the posts higher up in the thread for references.

It's quite simple. If a god can't predict the outcome from a system it doesn't know everything. In fact, since all events can be said to be outcomes from a system, a god which can't predict outcomes is a god which knows nothing.

It's quite simple. If a god can't predict the outcome from a system is doesn't know everything.

This is false. God can foreknow an event without predicting it: that is the very distinction I am making.

In fact, since all events can be said to be outcomes from a system, a god which can't predict outcomes is a god which knows nothing.

But your assumption is false: not all events are "outcomes from a system" in any sense relevant here. Human free choices (in the libertarian sense) are among those: they may be foreknown directly by an omniscient being with certainty, but because they are not the inevitable outcome of prior events, they cannot be predicted (that is, inferred from prior states of affairs) with certainty.

I think you'll find that the argument for the second of Andrew's atatements is the subject of this blog.

Since the soundness of that argument is the central point in dispute between us here, you can hardly expect me to be moved by the consideration that we disagree.

Personally, I'd have thought that a god which does not know the outcome from a system is self-evidently not omniscient. The clue is in the phrase 'does not know'.

But this is a misrepresentation of my position. If you will search carefully through the comments on this thread, you will discover that I have never said that God does not know the future, only that, as I just said in response to Andrew, he knows it directly as opposed to inferring or calculating it.

Since the soundness of that argument is the central point in dispute between us here, you can hardly expect me to be moved by the consideration that we disagree.

Then you write:

In that case I'm baffled by your request for Andrew to repeat the entire argument of the blog which you were discussing.

But I have not asked him for that: I have asked him whether he has any argument for his two claims. He presented his analysis as a short and easy way of reaching your conclusion. Since I have argued both by examples and by modal logic that your original argument is flawed, I am interested to know whether he has any argument other than the one you presented. If he has to fall back on yours, well, that's settled.

You also write:

Ah! So your god DOES know your decision before you make it, and it's always known it.

I am puzzled by the air of discovery suggested by your capitalization of the word "does." I have been saying this consistently since my first post at 14 November 2010 18:57.

You continue:

In that case you now have to explain how you could make a different decision and your god still be omniscient.

I have explained this multiple times: see above at 15 November 2010 21:15, for example. You have not, so far as I can see, even understood this response; all of your rejoinders seem to be either misrepresentations of things that I have said very clearly or variations on the (re)assertion that your original argument really is cogent. See, for example, your claim on 16 November 2010 18:35 that I had not answered your question (which I had), your claim at 18 November 2010 08:52 that it wasn't fair of me to answer your question and then point out that from my answer you cannot infer what you wish to infer (with the mistaken suggestion that I was claiming my answer wasn't an answer to your original question), your misrepresentation of my position in your note of 18 November 2010 18:45 (complete with the personal insult at the end), your repetition of the misrepresentation at 19 November 2010 09:38 (complete with the insult about a "heap of verbiage"), etc.

I welcome thoughtful interaction with what I have actually said. And I would welcome thoughtful discussion of any of the literature on this subject that I listed in my comment at 27 November 2010 14:43. But neither repeated misrepresentations nor mere foot-stomping will advance the discussion.

As before, you now appearing to be arguing that your god IS omniscient because it knows everything, but it doesn't know what your decision is until after you've made it, at which point it knows your decision and so becomes omniscient again.

I think it's plain that you know you can't escape the logic of the argument but you've managed to convince yourself that you've found a workaround which enables you to hold two diametrically opposed views simultaneously, either of which can be produced as the need arises, so you don't need to face the inevitable conclusion of the nasty logic, which is:

Either:

Your god is omniscient and you don’t have free will – and the Bible is wrong.

Or

You have free will and your god isn’t omniscient - and the Bible is wrong.

I suspect it’s the inevitable conclusion from either of which is preventing you from admitting the logic.

I would have to return the compliment on that one; it is clear to me that you aren’t following it at all.

As before, you now appearing to be arguing that your god IS omniscient because it knows everything, but it doesn't know what your decision is until after you've made it, at which point it knows your decision and so becomes omniscient again.

I have already dealt with this misunderstanding above. See the note at 15 November 2010 21:15, where I wrote, in part:

You will do X. God knows (and has known) that you will do X. You are free to do Y instead of X. But if you were to do Y, then it would have been the case all along that God knew that you would do Y. No contradiction emerges at any point. [Emphasis added]

If God would have known all along that you were going to do Y, then obviously God isn’t discovering it.

Does it seem appropriate to you to throw around an insult like this when your criticism depends critically on your failure to pay attention to verb tenses in what I have written?

I think it's plain that you know you can't escape the logic of the argument but you've managed to convince yourself that you've found a workaround which enables you to hold two diametrically opposed views simultaneously, either of which can be produced as the need arises, so you don't need to face the inevitable conclusion of the nasty logic, which is:

Either:

Your god is omniscient and you don’t have free will – and the Bible is wrong.

Or

You have free will and your god isn’t omniscient - and the Bible is wrong.

I suspect it’s the inevitable conclusion from either of which is preventing you from admitting the logic.

Rosa, in the absence of any actual fair-minded engagement either with my argument, or with the literature I have cited, this kind of rhetoric is just that -- empty grandstanding. You are free (!) if you like to continue to believe that your argument is a shining piece of logical rigor and that all Christians are simply idiots. But you must not expect people who have actually looked into these issues -- who have studied modal logic, who have read the relevant literature, and who make distinctions you refuse to observe -- to be impressed with your foot-stomping insistence that you are right.

>You will do X. God knows (and has known) that you will do X. You are free to do Y instead of X. But if you were to do Y, then it would have been the case all along that God knew that you would do Y. No contradiction emerges at any point. [Emphasis added]<

Can you really not see that what you're saying there is that your god's 'knowledge' changes if you change your decision?

Can you really not see that what you're saying there is that your god's 'knowledge' changes if you change your decision?

This isn't what I am saying at all. Your inability to distinguish what I am saying from what you have written above is, I think, the central difficulty that you are having in understanding what I am claiming.

In this world -- call it world 0, or w0 for short -- God knows today that you will, in fact do X rather than (incompatible action) Y tomorrow.

For you to be free to do otherwise is, by definition, for there to be some other possible world -- call it w1 -- in which you do, in fact, do Y rather than X.

It does not follow from these two claims that in w1, God (now falsely) believes that you will do X and you trick Him by doing Y. Rather, the standard and well-established position is that in w1, God has all along believed, correctly, that you will do Y.

Breaking it down:

In w0, God knows today that you will choose to do X tomorrow, and you do in fact choose to do X tomorrow.

In w1, God knows today that you will choose to do Y tomorrow, and you do in fact choose to do Y tomorrow.

World w1 is possible relative to w0. (I mean this simply in terms of the relative possibility relation in standard Kripke semantics for possible worlds.) In virtue of this, your action in w0 is free: the existence of a world that is possible relative to w0 in which you do Y rather than X fulfills the definition of libertarian freedom for your choice to do X, namely, that you could have done otherwise. If the relative possibility relation is symmetrical, then the model fulfills the definition both directions: your choice in w1 to do Y is also free. In S5, the most common modal system, the relative possibility relation is reflexive, symmetric, and transitive.

In neither world is God mistaken about what you do. In both worlds, your choice is free.

Actually, I have been saying the same thing since my first post here. The implication that I have shifted my position is completely unwarranted.

... that when you choose, like Schrodinger's Cat, you and your god discover what alternative reality you are both in,

Rosa, can you give any evidence whatsoever for your characterization of my position as one in which God discovers anything? If you cannot, would you consider actually reading what I have written carefully enough to avoid these crude and bizarre mischaracterizations?

... but it is always the one in which your god was right.

Yes, God is always right. That much you actually have properly understood.

And in this way your god can be both surprised by your decision ...

Nope. God is never surprised. I have no idea why you would think this follows from anything that I have said.

I think this discussion just ran over the edge of rationality into some sort of surreal alternative.

You're welcome to provide some supporting argumentation and evidence for your position. But until you do, you are not entitled to have it regarded as established fact.

I supose I should thank you for showing the absurd mental gymnastics needed to cope with the cognitive dissonance of holding two diametrically opposed views simultaneously and showing how you need to do that to retain your proud god delusion.

Saying it won't make it so. I have provided you with arguments; I have provided you with the technical formulations of the arguments using the best available modern formal tools; I have provided you with a bibliography.

And you have ignored it all, brushing it aside with a few snide comments about "verbiage."

You can't even be bothered to read what I have written carefully enough to characterize it correctly. You are providing a disturbingly good case that your reasoning takes the following form:

Tim disagrees with me.

Therefore,

Tim must be wrong.

Therefore,

Tim must be saying something stupid.

Here's something that sounds stupid.

Therefore,

It must be what Tim is saying.

I have lost count of the number of instances in this thread that fit this dismal pattern.

You may believe what you like. But you have made it abundantly evident that you do not know what you are talking about and are not willing to put in even minimal effort to correct that state of affairs.

This wil be my and your last comment on this thread since you are clearly unable or unwilling to grasp the simple concept that, no matter how 'clever' you imagine your 'technical formulation' to be, if it fails the simple test of not reaching absurd conclusions, then it is false.

You appear to believe that if you can come up with a 'technical formulation' with which to prove that black is white of indeed any colour you want it to be to serve the needs of your argument at the time, it must be right.

It is clearly absurd to argue that a god can be omniscient yet not know something, and that alone should have told you there was something wrong with your 'technical formulation'. Your test appears to be that it allows you to arrive at the required conclusion.

I'm afraid your requirements do not determine what is logical no matter how important you think you are nor how earnestly you wish it did.

Rosa, it seems you are unwilling to consider any counterclaims or arguments, and instead prefer strawmen. It is also clear that you do not understand contemporary philosophy; this is a must in order to have this debate. Modal logic is just the logic of the possible and the necessary, so that to say something is necessarily not possible in the face of a possiblistic formulation is to beg the question. Your dismissal of Tim behind rhetoric masks the lack of philosophical training. I am not trying to be rude, but this may help you in the future.

Sorry but I don't think there is any escaping the conclusion that a logical contruction which leads to a patently absurd conclusion is itself absurd, no matter how clever or elegant it's construction may have been.

If you can conclude that a god can be omniscient yet not know everything then your logic... well... isn't, no matter how fervently you wish it was and even if its failure strikes at the heart of a much-cherished superstition.

BTW, Arthur, I note your attempt to invoke the 'special needs' clause to exempt your god from normal logic. You may like to read my blog "The Special Needs God of Creationism".

I believe Tim has provided lucidly sound arguments (both in technical and in layman’s terms) for the compatibility between Omniscience and Freewill. Based on your characterizations of Tim’s arguments it does not appear that you’ve fully understood them. In the interest of advancing the dialog I’m offering to walk you any line of Tim’s argument dated “19 November 2010 01:06”, that may not have been clear to you. In that vein, do you mind paraphrasing what you believe he said in that post?

Yes I'd be delighted to hear a cogent explanation of how a god can be omniscient whilst not knowing everything, preferably without me being required to hold two mutually exclusive views simultaneously.

FYI, your scientific facts are wrong as to whom uses the bible. The entire bible is used by Christians. Jews are still waiting for their messiah- so the new testament of the bible is irrelevant. The Muslims utilize the koran.

The two mutually exclusive things both you and your alter ego Tim require me to believe simultaneously are:

1. Your god is omniscient, i.e., it knows all things and has always known them.

2. We can decide to do something other that what your god has always know we would do.

If you can get passed that without your usual fudge carefully covered by a heap of verbiage, or complaining that my refusal to do so is unfair and unreasonable, then please do so, as I have yet to see it done.

Hi again Rosa. I find it remarkable that despite multiple opportunities to do so you have yet to provide the *exact set of quotes* from Tim’s “19 November 2010 01:06" post which you believe contradict each other. What you’ve done instead is state what you *think* Tim said. The twain are not the same :-)

Perhaps I misunderstood you and you were saying all along that a god can't be inerrantly omniscient if it doesn't know our decisions before we make them.

And I thought you were disagreeing with me but just finding it difficult to put clearly, so trying to hide your difficulty under a tangle of verbiage.

I'm glad we've cleared that one up. I can understand your annoyance at being thought to hold two mutually exclusive views simultaneously through fear of what an invisible magic man in the sky might do if you were rational.

I am surprised to read this article by Rosa because it's in the strains of an article I wrote on my blog regarding godly love and free choice and the inherent fallacy involved: http://borici.blogspot.com/2011/04/two-fundamental-problems-with.html

I am not surprised in the context of when you came up first with it, but rather I'm happy with the fact that few other people, to my knowledge, attack the fundamentals of monotheism, rather than merely attacking existence arguments, such as is the case in almost all public debates...

Let’s recap. On “10 April 2011 15:35” I asked whether you could paraphrase what you believed Tim said in his “19 November 2010 01:06 post. You responded in part on “10 April 2011 16:57” asserting that Tim’s arguing required you “to hold two mutually exclusive views simultaneously”. Despite at least three separate requests that you produce any contradictory quotes from Tim’s “19 November 2010 01:06" post you have not done so.

It seems then that you have not provided the evidence required in order to demonstrably conclude that Tim’s “19 November 2010 01:06" post contains a contradiction.

@Rosa:” Perhaps I misunderstood”

It seems so. Erring on the side of explicitness… It seems that your assumption, that Tim’s “19 November 2010 01:06" post contains a contradiction, is based on your misunderstanding of what he wrote.

@Rosa:”a tangle of verbiage”

Do you mind sharing which quotes you found difficult to understand? Like I said on “10 April 2011 15:35” I’m offering to walk you through any line of Tim’s argument.

Great question, may I suggest perhaps that Foreknowledge does not imply Predestination. I maybe wrong but here’s how I got there.

Let me posit a potential scenario: You and I go to the horse races. We’ve been following our favorite horse for years. His name is Lucky. He’s been trained by the best. He reserves his energy till that last lap and then he turns on the juice. We bet on him to win. The race starts, but as the horses go into the last lap Lucky decides to be obstinate and refuses to put in extra effort and loses the race by 10 yards to a horse named Gimp.

We are bummed and head out of the stands. Suddenly a gray haired man shows up. He claims to be Dr. Emmett Brown. He assures us that he can take us 20 mins into the past. We hop into his DeLorean and we go back 20 mins. It’s the beginning of the race. Avoiding our former selves, we go to the window to make a new bet.

Questions:

1. Who should you bet on? (I’d say Gimp).2. Does Lucky have the freewill to do what his wants this race and put in that extra effort? (I’d say yes).3. Does your foreknowledge of Lucky’s choice force Lucky to do it again? (I’d say ‘No, your foreknowledge will not affect Lucky in anyway! Just because you know what Lucky is going to do does not mean you MADE Lucky do that. Lucky remains an independent freewill agent. Lucky remains responsible for his own choices.’

In other words Lucky is not influenced by your knowledge of what he is going to do. Foreknowledge does not imply predestination.

In this example as in the question, we presume that we are not postulating that there will be quantum universes caused by our rip in the time fabric when we returned thru the Time Machine wormhole. The time travel example is merely to provide an idea of a possible scenario. The real scenario maybe different.

E.g. At the point of the Big Bang there was no time or space. Thus whatever created the Big Bang (we are postulating it’s God) must exist causally (that’s cause-all not casually) prior to time and space. Thus, whatever created the Big Bang must be extra dimensional. Perhaps this thing views time the same way as we view a square all at once. This “thing” could then possibly be omnipresent in time and space. Thus the creator’s foreknowledge need not be one that predestines anyone. Note that does not mean that a creator that predestines people is not also possible, just not required.

So in summary Lucky had freewill, Lucky has freewill and Lucky will have freewill. I could be wrong but it seems that foreknowledge does not necessarily imply predestination.

Tim. As I said, if I've misunderstood your position all along and that you agree a god can't both be omniscient and not inerrantly know our choices in advance, then I'm happy to accept your correction.

However, if you require me to believe that a god CAN be inerrantly omniscient and not know something simultaneously then I'm afraid I can't be that intellectually dishonest. Continually whining about me not being dishonest enough to agree with you won't change that, I'm afraid.

No amount of verbiage or smoke-screens asking me to provide a non-existent quote to divert attention from your difficulty is going to change that, no matter what you call yourself.

As to the deism question. OK let me think. In the example, I previously dreamed up, you did not participate in the events. Yet thinking about it, it seems that it follows logically that if you had that power you could tweak events or even participate in certain events to ensure that certain of your plans/prophecies come to pass, all without interfering in the natural consequences of the free agent’s freewill choices. For instance, in the example, let’s assume you went back 4 years and ensured that Gimp was sent to the trainer who would be the one who was able to ensure that Gimp could feasibly win against Lucky. Thus ensuring that Lucky would actually have to exercise his perseverance to win.

Now I have to admit in my example I did not use moral freewill, more of a motivational freewill. Yet most of the above discussions have been about moral freewill, not about what shirt one chose to wear. It’s more of an issue if one person chooses to hurt someone else. So it’s possible that you as a time traveller could go back in time and set up opportunities to make moral decisions even if you removed some of their opportunities to pick certain non-moral decisions. E.g. In the example above you removed Lucky’s option to NOT have to race against Gimp. In fact you could even keep going back and changing the trainer till you found the one that was able to give Gimp a fighting chance.

In fact, if one knows all contingencies one can plan accordingly without ever actually having to "tweak". It's sort of like building a network router, one knows the worst case way that each of the inputs ports can act and if you are good enough you can design a router that does what you want it the first time.

That is an admission that Tim’s “19 November 2010 01:06" does not contain a contradiction. The reason I’m coming to that conclusion is that on “10 April 2011 15:35” I asked whether you could paraphrase what you believed Tim said in his “19 November 2010 01:06 post. You responded in part on “10 April 2011 16:57” asserting that Tim’s arguing required you “to hold two mutually exclusive views simultaneously”. Despite at least four separate requests that you produce any contradictory quotes from Tim’s “19 November 2010 01:06" post you have not done so.

We, you and I, know you are absolutely correct. No matter how many times I spin, flip, or rethink a decision prior to my final choice, if predetermined, eliminates free-will; if not, my choice has put the claim of omniscience in the dust bin of mythology. But, you knew this for you dug it up and dusted it off for this demonstration. Thanks.

Tim. As I've said twice now, I'm happy to be corrected and accept that somewhere under your heap of verbiage you agreed with me and acknowledged that a god can not be omnicience whilst ignorant about your decisions, and that a god which IS ignorant of anything can not be omniscient.

However, if you require me to hold the two mutually exclusive opinions simultaneously that a god is omniscient and the same god is ignorant about something, then I'm afraid intellectual integrity forbids me from doing that.

Hopefully this will have put the matter to bed, whether you call yourself Tim or joesephtime or indeed go by any other pseudonym so it looks like someone else supports you.

In my example Lucky could make any decision it wanted. The only limitation would be which set of decisions Lucky would be given. But Lucky could still decide freely between those decisions.

So maybe I misunderstood your statement. A decision by the omniscient being if predetermined, eliminates free-will?

This seems incorrect because the omniscient being could predetermine to give you an option A or Option B and know as the Time Travel example shows that the being would KNOW what choice you were going to take without ever impinging on your freewill.

However at no time does God know P or does God know T. You state "Let G(X) = God knows that X;" You haven't defined X until after the fact by seeing what happens first. If God knew X and it was definitive, then your undefined X would have occurred, but it didn't, instead either P or T occurred which you then substitute for the possibility X after the fact. What plays out in the conclusion has no bearing upon what God knows (X) because until it happens he lacks that assignment. That means that God did not know and he is as faulty as you or I.

The logic you're trying to describe should look like this:God knows that P will occurP = 1T = 2P occurs

Therefore T was never an option which God was going to allow. So you have no free will.

This is false: In w1, God has always known that P, and in w2, God has always known that T. I'm sorry if that wasn't plain.

You seem to think, though, that this fact is problematic. You write:

You state "Let G(X) = God knows that X;" You haven't defined X until after the fact by seeing what happens first.

I'm not sure what you mean here. This was a definition of a predicate, "G(X)." The "X" is a variable that can be filled in (truly or falsely) with any proposition.

If God knew X and it was definitive, then your undefined X would have occurred, but it didn't, ...

In which of these two worlds, w1, w2, do you think that God knew something that did not, in fact, happen? The whole point of the example is that this model shows the consistency of this sort of foreknowledge with the possibility of one's doing otherwise: what's possible in one world is actually the case in a different possible world.

You seem to be assuming, on the contrary, that what's possible in this world has to be actually the case in this very same world. But that move would erase the modal distinction between the possible and the actual.

"I'm not sure what you mean here. This was a definition of a predicate, "G(X)." The "X" is a variable that can be filled in (truly or falsely) with any proposition. "

That was my point.

X is a variable that can be filled in by what happens. By that logic, anyone can be a god. I can easily tell you about what variables exist, if I get one right, I'm god. That's why people make predictions, so they can appear supernatural.

You then replace the variable X with the possibilities, G(P) OR G(T). All you've done is list the possibilities and then say that, depending upon which one happens, God knew all the time. He didn't, he knew the variable X, which is the list of possibilities [G(P) OR G(T)].

G(X) = [G(P) OR G(T)]

That's the same logic that applies to observant humans.

You then say that if G(P) occurred then T was a possibility, if G(T) occurred then P was a possibility, to attempt to put some logical soundness into your argument, but both are completely irrelevant. If something which was a possibility does not occur, then it is still a possibility by definition. So what? Your logic still has God knowing a list of possibilities.

You see such logic as sound, by creating "world's" out of the possibilities where God knew a definitive all the time. He didn't. By your own logic (and ironically by mine) the best that God could do is know a list of possibilities, therefore not all knowing.

The point remains, if God knows ahead of time what choice you'll make then it was already determined and you have no free will.

What you've written doesn't seem to me to hang together. You agree that I was giving a definition of a predicate when I defined "G(X)," but then you write:

X is a variable that can be filled in by what happens. By that logic, anyone can be a god.

This baffles me. From what premises do you squeeze out that conclusion? Your following two sentences are completely obscure to me. Why would you say that people make predictions so they can appear supernatural? Do you think this applies to the meteorologist on the local weather channel -- that he's trying to appear supernatural?

You go on:

You then replace the variable X with the possibilities, G(P) OR G(T).

Actually, just "P" and "T" are the arguments that can be substituted for "X" here.

All you've done is list the possibilities and then say that, depending upon which one happens, God knew all the time.

I'm not sure what your point is in starting with "All you've done," but it is part of the definition of omniscience that for all X, if X, then G(X).

He didn't, he knew the variable X, which is the list of possibilities [G(P) OR G(T)]

Again, I believe you mean "P" and "T" there rather than "G(P)" and "G(T)" -- but let that go. I am not understanding your complaint. If you are merely saying that it is not possible for God to know the truth-value of a future tense claim regarding the action of a free agent, then your objection begs the question: that is the very point at issue, and it is the point that a possible worlds analysis resolves decisively.

You try to do something with the symbols when you write:

G(X) = [G(P) OR G(T)]

But this expression is just syntactic gibberish. "G(X)" is an open sentence, where the "X" functions rather like a pronoun with no antecedent.

You then say that if G(P) occurred then T was a possibility, if G(T) occurred then P was a possibility, to attempt to put some logical soundness into your argument ...

I'm sorry, but from this point it all goes downhill: it appears that you're just unfamiliar with modal logic. This is is a well-developed branch of modern logic, and nothing that I am doing here is particularly controversial. It would make our conversation more profitable if you would have a look at any good modern intermediate logic book that deals with modal logic, e.g. Sider's Logic for Philosophy, or Priest's Introduction to Non-Classical Logics, 2nd ed., or Garson's Modal Logic for Philosophers.

You're correct on that, I goofed and put [G(P) OR G(T)] instead of [P OR T], but my argument still stands. X is replaced in each of your models by P "OR" T not both.

My point is: In the context of an event, stating "God has always known P" establishes a rule that P must occur, or else God didn't know it. You can test the rule by asking the question: If God knows event P, what must occur? Anything other than the answer P renders "God knowing P" false. So:

G(P)∴P

You can add "not T, possibility T" and then plug T back into your predicate in a new world, but T wasn't part of the test for P. If we're testing P, then T is irrelevant to the argument. You can prove that T is invalid within the test for P by saying, "Let us assume P". By accepting P for testing you assume that P is the only possibility, therefore T cannot be a possibility within the same argument.

Even if you erroneously introduce T by virtue of the predicate you can clearly see that T was never a valid possibility in w1. T will never be able to occur in w1 because it renders G(P) false, therefore ◊T is invalid in w1.

Again, what you're left with is:

G(P)∴P

No other possibilities means you have no free will.

Now, you can assume the variable in the predicate is equivalent to the list of possibilities (otherwise it wouldn't be a variable) hence:

G(X)= [P OR T]

where God only knows the possibilities, in which case he's not omniscient.

Is there an argument associated with this:

for all X, if X, then G(X)

Such as: for all x, if x is true, then God knows x is true

P∴G(P)

Observant humans abide by that same logic. You again omit the event threshold. In the context of event P in your example, in order for P to be true it must first occur. Otherwise, prior to the event, the event is false. When P occurs and becomes true anyone observing the occurrence will know it.

The complex mental gymnastics required by theists to allow them to hold two mutually exclusive views simultaneously, never ceases to amaze me.

It should be self-evident to any rational person that a logical formulation which leads to the conclusion that God both knows everything and doesn't know something, is flawed.

No properly constructed logical argument can lead to two mutually contradictory conclusions and still be valid, no matter how satisfying it might be to those wishing to get past a fatal flaw in their belief system.

Yes, “G(P)” entails “P” – but what you go on to say doesn’t make any sense. “Testing P” isn’t the point; your use of this phrase makes it look like you’re conflating metaphysical and epistemic issues.

You can prove that T is invalid within the test for P by saying, "Let us assume P".

Invalidity is a property of arguments, not a property of propositions. Arguments may be either valid or invalid; propositions may be either true or false.

By accepting P for testing you assume that P is the only possibility, therefore T cannot be a possibility within the same argument.

This is just wrong.

Even if you erroneously introduce T by virtue of the predicate you can clearly see that T was never a valid possibility in w1. T will never be able to occur in w1 because it renders G(P) false, therefore ◊T is invalid in w1.

Again, propositions are neither valid nor invalid: they are either true or false. “T” is false at w1, but “◊T” is true at w1 in virtue of the fact that w2 is accessible from w1 and “T” is true at w2. Laying out possible worlds and specifying accessibility relations among them is the way that we model possibility in modal logic. Have a look at James Garson’s article on modal logic.

You again omit the event threshold. In the context of event P in your example, in order for P to be true it must first occur. Otherwise, prior to the event, the event is false. When P occurs and becomes true anyone observing the occurrence will know it.

I find these sentences obscure, so I may be misunderstanding you, but it seems you’re saying that all future-tense contingent statements must be false. This strikes me as a very odd claim, one that would play hob with our ordinary ways of speaking and thinking. How can you say to someone, “You were right!” if when he made his prediction it was, by this principle, false? Perhaps this is your way of trying to circumvent an argument for fatalism, but if so, I think it is needless and confusing. You can read more about fatalism and the various moves that philosophers have made with respect to it here.

Actually, I didn't goof. Perhaps G(X) = [G(P) OR G(T)] isn't the best way to represent this, but G(X) is your predicate for the two mutually exclusive assertions "G(P)" or "G(T)". God knows a definitive something P or God knows a definitive something T. In either case if what god knows is definitive then there are no other valid possibilities for that case except what god knows.

Athens said: "My point is: In the context of an event, stating "God has always known P" establishes a rule that P must occur, or else God didn't know it. You can test the rule by asking the question: If God knows event P, what must occur? Anything other than the answer P renders "God knowing P" false."

This is false.

In my mind, I have just picked what you're going to have for breakfast tomorrow. You may not have decided, but some time between now and then, you're going to make that decision. You may change that decision, several times, but by the time breakfast gets here, you're going to have to make a decision. You may even decide to skip breakfast entirely. Regardless, when breakfast arrives, you will have made a final decision. What if, that final decision matches what I've picked in my head right now? Have you lost your free will because I "knew" what you were going to decide? Of course not. Likewise, you don't lose your free will because God knows what you're going to decide. The difference between God and I is that I'm guessing, and God knows. Knowing ahead of time does not establish a rule the "P" must occur.

As I stated weeks ago, the problem isn't the statement, but the terms being used. Atheists see omniscience as predetermined, where Christians see omniscience as foreknowledge. There is a difference and Atheists refuse to acknowledge the difference. It's like playing a board game with a child who picks and chooses which rules to follow; they can't lose. Yes, the original question does work out as a contradiction when the rules for answering are limited to the rules that work for the atheist. But as we grow older, we need to accept that reality includes more rules than we sometimes like. When the question is posed allowing for the complete definition, which includes foreknowledge, the contradiction disappears.

I'm just speaking in plain old words now. Call me a child if you like, but all of the symbolism is hard for me to follow.

Here are my presumed facts based on G(P), which is "God knows Tim will eat (only) a pop-tart for breakfast":

Fact 1) Tim has freewill to make his own decisions.Fact 2) Freewill is the right to choose regardless of God's decision.Fact 3) God is all knowing.Fact 4) God makes the foreknowledge decision that Tim will eat only a pop-tart for breakfast.Fact 5) Foreknowledge is knowledge prior to an event.

Here is my presumed order of events occurring based upon the facts:

1) First, God makes his foreknowledge decision that Tim will eat only a pop-tart for breakfast.2) Next, Tim mulls over his possibilities, he can either have only a pop-tart or only toast.3) Next, Tim eats only a pop-tart for breakfast.4) Finally, it can be determined that God was correct, and I can accept that God is omniscient.

Now I have to ask myself a question: What would have happened at the point in time when Tim exercises his free will and eats only toast instead?

Asking myself the same question, this is how events seem to me to occur following along with your logic:

1) First, God makes his foreknowledge decision that Tim will eat only a pop-tart for breakfast.2) Next, Tim mulls over his possibilities, he can either have only a pop-tart or only toast.3) Next, exercising his free will to go against God's decision, Tim eats only toast for breakfast.4) Finally, Oops! God was wrong. God makes mistakes.5) So now we go back in time to correct God's mistake.6) God now makes his new foreknowledge decision that Tim will eat only toast for breakfast.7) Next, Tim mulls over his possibilities, he can either have only a pop-tart or only-toast.8) Next, Tim eats only toast for breakfast.9) Finally, God was correct, but only after having first made a mistake and having to go back in time to correct it.

In plain words, assuming G(P), can either of you give me your synopsis of the facts and events, as you see them?

1) God looks into the future and sees what Tim will, in fact, do. In fact, in this world, Tim will choose T; therefore, G(T). Then

2) Tim mulls over his possibilities and chooses, freely, which one to do. Ex hypothesi, in this world, it's T.

Since God already saw the future, he knew this already.

In order for Tim's choice of T in w1 to be free (in the libertarian sense), there must be another world, call it w2, that is possible relative to w1, in which Tim chooses P rather than T. So in w2:

1*) God looks into the future and sees what Tim will, in fact, do. In fact, in this world, Tim will choose P; therefore, G(P). Then

2*) Tim mulls over his possibilities and chooses, freely, which one to do. Ex hypothesi, in this world, it's P.

Since God already saw the future, he knew this already.

Objection 1: "But what if God guesses wrong? Until Tim makes his choice, even God doesn't know which world he is in -- w1 or w2."

Reply: The Christian view is that God is not guessing: he is seeing the future. So there is no possibility of his being wrong. This objection has force only against a caricature of the Christian position.

Reply: The problem here lies with the word "can't." It would be more accurate to say that Tim won't choose P in w1. After all, w1 is already defined as a world in which Tim chooses T, so of course in that world he doesn't also choose something incompatible with T. Tim's choice does determine which world we are in, w1 or w2. God's foreknowledge means that God knows, and has always known, which way Tim will choose.

I think you've come to the fundamental difference in the way we're thinking about this. You are conceiving of God's knowledge of the future along the lines of a human prediction -- but still, ultimately, a fantastically well-educated guess. And with any foreseeable extrapolation of human predictive ability (increased intelligence, increased data), such a guess about what a free agent will do in the future may turn out to be wrong.

If I thought that God's knowledge of the future were like that, then I would not say that God is certain about the future. But that is not the Christian concept of God.

As I wrote here half a year ago (15 November 2010 21:15):

You can complain, if you like, about omniscience; you can argue that no being could have that kind of knowledge. But you cannot generate a contradiction from the mere combination of freedom and foreknowledge.

Incidentally, I think that to be consistent you will have to deny that future-tense contingent statements about the free actions of free agents are true. For the reason why, see the parallel argument I give in this thread at 23 November 2010 23:44 (and the diagnosis of the flaw in the argument in the following comment).

You have free will until you make a decsion. Once you choose, you can't choose something other than what you choose. Can you choose something other than what you chose for breakfast yesterday? No, because you made a decsion. Likewise, you'll make a decision by breakfast tomorrow, breakfast will arrive, and you will no longer be able to choose something else.

God knows all the options you will have before tomorrow, and all the options that will run through your mind. You may choose a thousand different things by tomorrow, changing your mind by the minute. He can know all those decisions, as well as the final decision when breakfast will arrive when you will no longer be able to choose something other than what you choose. You will lose free will because time will run out.

I understand the logic with a great amount of clarity since Tim broke it down into words for me. I read the 23 November 2010 23:44 post. I've read Alan's point of view.

I was presented with:1) the logic offered by Tim; G(X) etc..2) for all x, if x, G(x)

I understand both items. I can rationalize them in my head: For every possibility, there is a world where God foresees that possibility and that possibility is true.

I'm suggesting: That quality is not omniscience. It DOES fit the definition "all knowing", but it doesn't fit any special abilities of God which any human doesn't already have.

I'll provide an example, Example 1a:I go into a store and I buy one ticket for each of all possible sets of numbers for the lottery because I have foreseen a world where each individual set will win. The next day, my set of numbers wins. (This is not very impressive knowledge to me.)

Example 2b:I go into a store and I play one set of numbers for the lottery, which I know will win because I have foreseen that my one set of numbers will win and none of the other sets will win. The next day, my set of numbers wins. (This is impressive knowledge to me.)

Example 2:I can imagine a world where Alan will have breakfast on June 15th 2011 or one where he won't. If he does have breakfast, I have imagined in my head all of the possible food selections, combinations, ingredient substitutions, non-edible consumption options, choke to death on first bite/no choke, all of the possible times of food/mouth contact, meal portions, chemical makeup variants, quantified caloric variants, whether or not he eats with company, where he eats, what angle the food enters his mouth, etc., etc., etc.. Alan, please post what happens for breakfast on June 15th 2011 and I will let you know which world we are in.

I'll say again that if God knows all of the possibilities pending what happens in real life, then there is just no point to God's knowledge at all. By my beliefs or yours, there is just no point to God for me. You've all helped me to reaffirm my beliefs. Thank you.

'Sorry, but actually, it does not follow. You will do X. God knows (and has known) that you will do X. You are free to do Y instead of X. But if you were to do Y, then it would have been the case all along that God knew that you would do Y. No contradiction emerges at any point.'

This is your argument, right? So in the first line, you say that God knows you will do X and in the second last line , he knows that you will do Y. That's a contradiction in itself. It's like a student who got the answer wrong in the exam saying that he knew while writing it that he is wrong, but wrote it anyway.

So, God knows that I'll post this comment, but he also knows that I won't post it if I decide not to. So either way, he'll be right. What you're ignorantly implying is that your god guesses everything and after one of them ineveitably turns out to be right, he claims that he knew all along.

"...you can do but you will not."

Just suppose a student asks a teacher whether he may go to the washroom in the middle of a class. And this is the teacher's response, "you can go but you will not." It's tantamount to saying, "you can go but you can't" both the sentences are a contradiction. Either way, the child doesn't have a free will. So intead of accepting Rosa's perfectly simple logic, you've created a paradox.

Yes. As I remarked before, the form of 'logic' being used here is that used by theology where the test of 'good' logic is that it produces the desired answer, even if it's an absurd one which requires one to hold two mutually contradictory opinions simultaneously.

Of course, this is not considered a problem for theists who will dismiss those sorts of problems as 'mysteries' beyond the ability of mere mortals to comprehend or understand.

Yes, they claim that bible has some scientific predictions, thus the bible is true. They feign to be oblivious to the fact that the same science has proven that the world didn't begin 6,000 years ago, thus shattering the very foundation of bible.

So they both trust science (when it matches their favorite religion) and do not trust it (when it doesn't match) creating yet another paradox.

Combine such contradictions, gaps and cherry-picking, and you get the logic of an average theist.

It is perhaps not the very wisest thing to start off a post by calling someone naive and then proceed to make a fool of yourself on the very point at issue. But as you please.

'Sorry, but actually, it does not follow. You will do X. God knows (and has known) that you will do X. You are free to do Y instead of X. But if you were to do Y, then it would have been the case all along that God knew that you would do Y. No contradiction emerges at any point.'

This is your argument, right?

No. It is a countermodel to the claim that Rosa and others have been putting forward. You do know the difference between an argument and a countermodel, right?

So in the first line, you say that God knows you will do X and in the second last line , he knows that you will do Y. That's a contradiction in itself. It's like a student who got the answer wrong in the exam saying that he knew while writing it that he is wrong, but wrote it anyway.

Wrong. A contradiction arises only if both propositions are true in the same possible world. If you don’t know what this means, please take the time to study modal logic before you make assertions like this. It will keep you from making statements like your next one:

So, God knows that I'll post this comment, but he also knows that I won't post it if I decide not to. So either way, he'll be right.

You’ve just conflated two distinct possible worlds.

What you're ignorantly implying ...

Oh dear, there you go again.

... is that your god guesses everything ...

Fail. See my explicit statement to the contrary in my comment dated 11 June 2011 13:51.

... and after one of them ineveitably turns out to be right, he claims that he knew all along.

Since this charge rests on a very elementary misunderstanding, it is irrelevant.

"...you can do but you will not."

Just suppose a student asks a teacher whether he may go to the washroom in the middle of a class. And this is the teacher's response, "you can go but you will not." It's tantamount to saying, "you can go but you can't" both the sentences are a contradiction.

The analogy is hopelessly bad. The student is requesting permission; if the teacher says “... but you will not,” either he is withdrawing permission or else he is making a prediction. In neither case is he analogous to God. So this line of approach is completely irrelevant.

Yes, very wise of me to call you naive because that's what you are.I'm not going to waste my time with you anymore, whatever you think of that.But just so you know, it's NOT an analogy. You should be 'wise' enough to see that.

It's just an example to show that the statement you made is an oxymoron. Even if "you can, you will not(ever)" refutes free will, whether you ask for the permission or not.

Very interesting comments. This is what I have learned about God being omniscient and granting us free will. God does a rewind in order to be able to say he was certain something was going to happen. I also learned He is very well aware of all the choices we have and then can say, See I knew it! It was world #4! I also learned that proving the existence of God is not as important as discussing or "arguing" the fundamentals of monotheism.

Rosa, you were so wrong in your statement: "These morally bankrupt Atheists (for that is what they are) are a disgrace to humanity."

People who know they need to use deceit and trickery to get you to believe in the god they promote can't themselves believe in it, or they wouldn't know they need to be dishonest. It's therefor fair and accurate to describe them as Atheists, much as it pains me to say so.

This is, of course, not a general comment on Atheists, of which I'm proud be be one, but on those Atheists who earn a living tricking gullible simpletons by selling them infantile superstition.

In fact, it's important that you not be able to, since otherwise anyone's knowledge of the past would render people's actions unfree by parallel reasoning. "I know that, in point of fact, he took the train. Could he have taken the bus instead?" etc. The argument works in both cases or in neither. In this case, it's neither."

This is ridiculously wrong. There is a massive difference between a posteriori knowledge of an event and alleged a priori knowledge of an event. Pretty mindless claim right there.

That includes what you choose to do. So an omniscient god is contradictory to our being able to do something that he doesn't expect.

Everything evil that happens, he knows it's going to happen. He made it all, and set it all up, and so therefore nothing that happens here can surprise him.

It's like winding up a clockwork toy and watching it go round and round in circles on the floor till it runs down.

The point is: why? What does he get out of it? How on earth can it enrich his existence, if he's so big and strong and clever?

The same question can be asked from the standpoint of a completely rational and deterministic universe as (I believe) Laplace imagined it. If you knew the trajectories of every particle in the universe and every force between those particles, you could predict the entire future state of everything, from the movement of galaxies to the detail of the flow of the chemical transmitters between the various specialised cells in your brain. And it's the latter that are in question here.

So for a completely rational deterministic universe there is no free will either.

The good news for the libertarians is that quantum physics proves that the universe is not deterministic but probabilistic. So our choices are ultimately the result of a quantum statistical process and in theory can not be predicted completely accurately (although in a lot of cases a fairly accurate guess can be made).

Another piece of good news for libertarians is that not even mathematics is completely closed and deterministic, as Godel proved at around the same time that quantum physics was evolving as a science. That is, there are mathematical statements (which can be made in a particular axiomatic framework) whose truth value can not be determined (in that axiomatic framework). This means you can't even determine for certain which mathematical models are going to be completely available to you when modelling the behaviour of the universe.

"So an omniscient god is contradictory to our being able to do something that he doesn't expect."

This statement is ambiguous. It could mean, If we take it to be mentioning what you will, in fact, do tomorrow (say, have an egg for breakfast), then God expects that. It does not follow that you couldn't do it; it just follows that, in fact, you won't.

In the other sense, it means, roughly, "Whatever you choose to do tomorrow, God expected that." This is true, but it doesn't follow that you weren't free to choose it.

"It's like winding up a clockwork toy and watching it go round and round in circles on the floor till it runs down."

In this context, that statement begs the question against the defender of libertarian free will.

"The good news for the libertarians is that quantum physics proves that the universe is not deterministic but probabilistic. So our choices are ultimately the result of a quantum statistical process and in theory can not be predicted completely accurately ..."

This statement presupposes that quantum theory is a complete description of physical reality, a point of view that has come under fire in the physics community in the last 20 years or so.

"Another piece of good news for libertarians is that not even mathematics is completely closed and deterministic ..."

"Deterministic" would not be a helpful term to use to describe a view of mathematics, where causal relations are not in question.

"This means you can't even determine for certain which mathematical models are going to be completely available to you when modelling the behaviour of the universe."

This claim is pretty obscure. What Gödel showed is that the consistency of any system rich enough to support elementary mathematics cannot be proved by finitary means. If you're cool with transfinite induction, you can do the job with that tool. But the tool is then much more powerful than elementary mathematics itself, and that raises interesting questions that haven't yet been resolved.

"Science has proven that God cannot be omniscient."

When you have a proof that God is restricted to doing mathematical proofs in finitary systems, let us all know.

I know you are convinced of your logic, but boolean logic is actually a large portion of my field as a computer scientist and your initial assertions about w1 are inherently flawed which is why the rest of your argument is falling down and causing the argument above.

◊T is not possible in w1 because G(P) is true. If God knows he will eat a pop-tart and if God is infallible then he will eat a pop-tart and T is not possible. I know you desperately want to create a quantum problem with other worlds, but that dodges the question because if we're living in w1 and G(P) turns out to be false in w1 then God is not infallible in w1.

You said: "Yes. He can [eat toast]. But he won't."

Why won't he? What prevents him from choosing toast?

If he has a 0% chance of choosing toast in w1 then he does not have freedom of choice in w1. If there is no possible way for him to choose to eat Toast then he doesn't have freedom of choice. If there IS a possible way for him to choose Toast in w1, how does it do it? How does he choose in w1 something which invalidates God's perfect foreknowledge?

This is the point where you are required to spiral into infinite quantumly possible worlds in order to justify your belief. The difference between your God/Pop-Tart/Toast problem and Schrödinger's cat is that the opposing quantum possibilities for the state of the cat are NOT defined before the act. When you assert that God has foreknowledge of what the choice will be you are already collapsing the quantum probabilities because the act has already been chosen.

It's interesting to me that in order to justify your beliefs that you need to invent (essentially) infinite universes in which every possible tiny choice for every single person now and throughout history are played out in all of their possible permutations such that the one we happen to be in just happens to be the one in which God _happened_ to be right for all possible choices.

I appreciate the straightforward nature of your criticism. Unfortunately, you have not understood what I am trying to say.

You write:

“I know you are convinced of your logic, but boolean logic is actually a large portion of my field as a computer scientist and your initial assertions about w1 are inherently flawed which is why the rest of your argument is falling down and causing the argument above.”

The proper technical tool here is modal logic, not Boolean logic.

“◊T is not possible in w1 because G(P) is true. If God knows he will eat a pop-tart and if God is infallible then he will eat a pop-tart and T is not possible.”

This is false. According to standard semantics for possible worlds, T is possible in w1 just in case there is some world wn, accessible from w1, in which T is true.

You might want to read up on this. Here’s a link to get you started:

http://en.wikipedia.org/wiki/Modal_logic#Semantics

“I know you desperately want to create a quantum problem with other worlds,”

Actually, quantum theory has nothing to do with the matter. See below.

“but that dodges the question because if we're living in w1 and G(P) turns out to be false in w1 then God is not infallible in w1.”

Sure. But G(P) is true in w1.

“You said: ‘Yes. He can [eat toast]. But he won't.’

Why won't he? What prevents him from choosing toast?”

Nothing. He simply doesn’t. As the majority of Christians understand it, divine foreknowledge isn’t a causal force. This is just a category mistake.

“If he has a 0% chance of choosing toast in w1 then he does not have freedom of choice in w1.”

First, 0% is not the same thing as logical impossibility, as any good text on measure theory explains.

Second, talk of probability must always be considered with reference to background knowledge. What bit of background would we need to invoke in order to get a “0% chance” here? That God knows that he will not eat toast? Okay – but in that case, the same consequence would follow from the claim that Kenny knows that he will not eat toast.

“If there is no possible way for him to choose to eat Toast”

Sure there is. But in w1, he doesn’t.

“then he doesn't have freedom of choice.”

This simply doesn’t follow.

“If there IS a possible way for him to choose Toast in w1, how does it do it?”

This question is muddled. Possible worlds are differentiated by the propositions that are true in them. Ex hypothesi, in w1, he doesn’t eat toast. What it means, in w1, for it to be possible for him to eat toast is that there is some world wn, accessible from w1, in which he does eat toast. That needn’t be w1.

“How does he choose in w1 something which invalidates God's perfect foreknowledge?”

Nobody invalidates God’s perfect foreknowledge.

“This is the point where you are required to spiral into infinite quantumly possible worlds in order to justify your belief.”

As I pointed out, this has nothing to do with quantum theory. You appear to be confusing the many worlds interpretation of quantum theory with Kripke semantics in modal logic.

“It's interesting to me that in order to justify your beliefs that you need to invent (essentially) infinite universes in which every possible tiny choice for every single person now and throughout history are played out in all of their possible permutations such that the one we happen to be in just happens to be the one in which God _happened_ to be right for all possible choices.”

I’m sorry to be blunt, but you obviously have no idea what modal logic is all about. Please read the link I gave you above. If your interest is piqued, you might want to grab a copy of Hughes and Cresswell, or Garson, or some other standard text on the subject.

For someone who doesn't follow this technical stuff, are you saying it is possible for you to do something a god didn't know you were going to do but that the god can still know everything? If so, why are the terms 'didn't know' and 'know everything' obviously contradictory yet don't contradict one another?

Since you phrase this in terms of “a god,” there is no clear answer until you stipulate whether you are using the term “god” in a manner that builds in the notion of complete foreknowledge. If you are, then, since I hold that future-tense claims have present truth values, I should say:

1. There are things – call them Xa, ..., Xn – that I will, in fact, do in this world – call it w1.

2. There are (inter alia) possible worlds wa, ..., wn, accessible to w1, in which, respectively, I do not do Xa, ..., Xn.

Therefore,

3. In w1, for each of those acts Xa, ..., Xn, I could have done otherwise. (By def., from 1, 2)

Therefore,

4. In w1, I perform each act Xa, ..., Xn freely.

5. In w1, God knows, that I will perform Xa, ..., Xn.

However, In wa, ..., wn, God knows that I do not perform Xa, ..., Xn, respectively. There is no world in which I perform an action that catches God by surprise.

So the direct answer to your question, “are you saying it is possible for you to do something a god didn't know you were going to do but that the god can still know everything?” is that the question is ambiguous. If you mean,

Q1: “Is there a possible world in which you perform an action that an omniscient being did not know you were going to do?”

then the answer is “No.” But if you mean,

Q2: “Can there be something you do not in fact do, that God knows you do not do, and it nevertheless be possible that you do it?”

then the answer is, “Yes.” It is possible because in some other possible world, accessible from this world, I do in fact do the thing in question.

In other words, your logic leads you to two opposite and contradictory answers.

Do you really not see the problem there?

To me the question is quite simple: Either the god in question knows everything and so there is nothing you can do which it didn't know you would do, or there are things you can do which it didn't know about and so it can't know everything.

In other words, either the god in question is omniscient and you don't have free will, or you have free will and the god isn't omniscient. The two mutually exclusive conditions can't co-exist in the same universe.

In words ordinary people can understand, can you please point out the fallacy there, if there is one.

No, Rosa, I do not -- all I see is your oft-reiterated but unsubstantiated and groundless charge that there is a contradiction here. In my judgment, you are simply confused by the surface grammar of English and do no recognize the ambiguity in your own attempts to formulate your challenge. Pace Wittgenstein, ordinary language is not in perfect logical order as it stands.

I do wish you would bother to learn some modal logic so that you could engage with the argument with the precision afforded by the proper technical tools.

"In other words, either the god in question is omniscient and you don't have free will, or you have free will and the god isn't omniscient. The two mutually exclusive conditions can't co-exist in the same universe."

This is simply a statement of your conclusion, not an argument for it.

"In words ordinary people can understand, can you please point out the fallacy there, if there is one."

No. It's a statement of the paradox you are being asked to explain and which you are simply waving aside as not a paradox. All I am doing is asking you to explain in simple English how these two mutually exclusive and contradictory ideas can both be true.

It's interesting to me that in order to justify your beliefs that you need to invent infinite universes in which every possible tiny choice for every single person now and throughout history are played out in all of their possible permutations such that the one we happen to be in just happens to be the one in which God _happened_ to be right for all possible choices.

"It's interesting to me that in order to justify your beliefs that you need to invent infinite universes . . ."

As I pointed out above, this is just a misunderstanding on your part based on your conflation of the many worlds interpretation of quantum theory with the technical device of possible worlds in modal logic.

Across this inifinite multi-verse where all of humanity currently living, all of humanity now dead and all of humanity yet to live have all possible tiny permutations played out for all possible tiny choices they'll make throughout their entire lives...

Are you saying that Kenny(1), Kenny(2), .... Kenny(n) are the SAME person? That there is only one Kenny in all of these universes?

"Well, I'm sorry but if you can't see that two opposite and mutually exclusive ideas are not contradictory then you are obviously using a private definition of the word 'contradictory'."

For my part, I'm sorry that you're unable to see that the two claims are not contradictory, and I'm doubly sorry that you keep repeating the claim that they are without either providing a cogent argument for the claim or attempting to engage seriously with one of the numerous explanations I have given you.

You cannot win an argument simply by insisting that you are right. Misrepresenting your opponents as having a "private definition of the word 'contradictory'" when they disagree with you about the substantive point of whether the two claims are contradictory is neither fair nor honest.

"if you can't see that a god who knows everything and at the same time in the same universe doesn't know something ..."

Why should anyone find this misrepresentation of my clearly stated position, which is visible above on this very page, not to be dishonest -- and find your resorting to it to be an admission that you are unable to engage in rational discussion and argument?

Seriously. You cannot win an argument by putting words into your opponents' mouths that are the very opposite of what they have repeatedly and clearly claimed in public.

In what sense of the word 'misrepresenting' was stating the question you are struggling to answer misrepresenting the discussion, please? And in what sense of the words 'putting words into your mouth' was restating the subject of the discussion putting words into your mouth, please?

Or are you merely seeking an excuse to abandon your argument and flounce off in indignation rather than having the good grace and integrity to admit you can't construct a logical refutation of the proposition?

"In what sense of the word 'misrepresenting' was stating the question you are struggling to answer misrepresenting the discussion, please?"

It was when you wrote:

"Well Tim, if you can't see that a god who knows everything and at the same time in the same universe doesn't know something, is not contradictory then that may explain your difficulty."

Several times in this discussion have I told you that it is never the case that God doesn't know something.

For example, see 19 November 2010 01:06, where I wrote:

"The only constraint imposed by omniscience is that, in any given world, if a proposition is true, then, in that world, God knows that proposition; whereas if, in that world, a proposition is false, then, in that world, God does not believe that proposition."

Or see 7 April 2011 13:21, where I wrote:

"I have never said that God does not know the future, only that, as I just said in response to Andrew, he knows it directly as opposed to inferring or calculating it."

You huff:

"Or are you merely seeking an excuse to abandon your argument and flounce off in indignation rather than having the good grace and integrity to admit you can't construct a logical refutation of the proposition?"

Do you think that, by continuing to pretend that you know what you are talking about, you will confuse anyone who actually takes the trouble to read through and understand this entire thread?

There is something very strange about your inability to see the bankruptcy of your argument even after it has been explained both formally and informally. I have to admit, when I think of you, "good grace" and "integrity" are not the first terms that come to mind.

Tim, sorry I couldn't respond earlier, Google won't let me login via my iPad so I had to wait until I was back at my desk. I read through the information about Modal Logic and several related pages. I still see several problems with this twisted attempt at logic.

First, even the page you referenced discussions the contradictory and controversial nature of arguments framed in this possible-worlds logic.

Secondly, while it may offer some seriously whack conversations which remind me of 3am college freshman discussions, it's not in any manner a practical answer to the question at hand and I think it's disingenuous to put it forth as such. There is only one actual world and in this singular actual world all of the "decisions" are supposedly already known and pre-determined because God supposedly already knows them. Meaning that in this one actual world, a person can't actually choose Toast or Pop Tart because in this one actual world God supposedly already knows the outcome which means it's pre-determined... which means that there is only one outcome in this one actual world... which means there isn't a choice in this world.

Lastly, you accuse Rosa of wrongly asserting there is a contradiction... when in every manner of looking at this question it is OBVIOUSLY contradictory... except for this one, seriously weird and self-admittedly controversial method of philosophical discussion... a method of philosophical which is rejected by many philosophers.

“Secondly, while it may offer some seriously whack conversations which remind me of 3am college freshman discussions, it's not in any manner a practical answer to the question at hand and I think it's disingenuous to put it forth as such.”

Neither your subjective reaction to modal logic, which by your own confession you have just begun to learn about, nor your personal estimation of my integrity does anything to advance the argument.

“There is only one actual world and in this singular actual world all of the ‘decisions’ are supposedly already known and pre-determined because God supposedly already knows them.

Known, yes. Predetermined? That depends on what you mean by the term.

“Meaning that in this one actual world, a person can’t actually choose Toast or Pop Tart”

Of course one can – we do it all the time.

“... because in this one actual world God supposedly already knows the outcome which means it’s pre-determined...”

If that is all that you mean by “pre-determined, well and good.

“... which means that there is only one outcome in this one actual world...”

Did anyone think there were two incompatible outcomes in this world?

“... which means there isn’t a choice in this world.”

That doesn’t follow. You need to think seriously and rigorously about what it would mean for something to be false but possible in this world.

“Lastly, you accuse Rosa of wrongly asserting there is a contradiction... when in every manner of looking at this question it is OBVIOUSLY contradictory... except for this one, seriously weird and self-admittedly controversial method of philosophical discussion... a method of philosophical which is rejected by many philosophers.”

1. What’s wrong with Rosa’s substitution of foot-stomping for dialogue is that whether there is a contradiction is the very point in dispute between us.

2. What is most controversial in modal logic is not something that arises in the argument under discussion here.

What I mean by the term is the english definition of the term as well as the way it is standardly used in these discussions. If you'd like to just redefine english, then I'm sure we can also prove that God is firetruck.

"Of course one can – we do it all the time." (re: choosing)

Of course, I agree with you here because I have seen absolutely no evidence for the existence of any God which means there isn't any sort of foreknowledge of what we're going to do... however, when you try to assert there is an omniscient God who knows what I'm going to have for breakfast, then there is necessarily one and only one outcome to that event which means I don't actually have a choice, merely the illusion of choice.

The whackness that is introduced this philosophical modal logic is that to start I can prove that it's possible I'm standing in a hail storm even though I'm currently in 70 and sunny in southern California. That's possible in some other world, so it's "possible" but obviously contradictory to the actual world. Then when you try to jam a concept like omniscience into this whack logical structure you make it even stranger and more contradictory because you push part of it into the future with supposedly perfect foreknowledge in the present and use that as an attempt to prove your assertion is true... but the same logic says that it's possible I'm standing in hail even though I'm CLEARLY NOT.

“What I mean by the term is the english definition of the term as well as the way it is standardly used in these discussions. If you'd like to just redefine english, then I'm sure we can also prove that God is firetruck.”

That is a truly foolish comment. Ordinary English is often ambiguous; we have to make distinctions and clarify terms if we want to reason precisely. The ambiguity here on “X is determined,” where X is some future-tense statement, is the ambiguity between:

D1: “It is true now that X”

and

D2: “It is not possible that not-X”

The former I grant, but it is innocuous. The latter is question begging in this discussion.

“when you try to assert there is an omniscient God who knows what I'm going to have for breakfast, then there is necessarily one and only one outcome to that event which means I don't actually have a choice, merely the illusion of choice.”

This objection has been covered several times over in the thread above. From

□(If God knows that p, then p)

it does not follow that

(If God knows that p, then □p).

“The whackness that is introduced this philosophical modal logic is that to start I can prove that it's possible I'm standing in a hail storm even though I'm currently in 70 and sunny in southern California.”

You appear to be confusing epistemic probability with logical possibility.

You should already be clear on the definitions of omniscience, predetermination and foreknowledge considering they are littered throughout this conversation. If you aren't, then you shouldn't have been in this conversation from the beginning.

"This objection has been covered several times over in the thread above."

And every time has been rejected because your modal logic is contradictory to reality using every other logical method or system of knowledge. It's unhelpful, impractical. If your modal "logic" shows that it's possible that it is hailing while I'm standing in the sun shine, it's clearly not very helpful.

The charge is that the Christian conception of divine foreknowledge is incompatible with libertarian free will. Therefore, the Christian definition of foreknowledge and the libertarian definition of free will are the ones on the table. Making up alternative definitions and then crowing that those are incompatible is simply opting out of the rational discussion.

You still have not answered the question about false but possible propositions. Many things are false, even obviously false, that are also possible. Your reasoning from your example about the rain is simply a confusion; the idea of its being possible is not "... but maybe I'm wrong" (an epistemic worry) but rather "... but this state of affairs is not logically necessitated" (a matter of alethic modalities).

I see that you continue to rant about modal logic. Good. It's useful to see that in order to stand by this faulty argument, you have to ditch an entire branch of modern logic. For anyone who actually understands what is going on in modal logic who comes along and reads this thread in the future, that point will be crystal clear.

"Making up alternative definitions and then crowing that those are incompatible is simply opting out of the rational discussion."

That's nice, but I haven't done that. You're the one who seems to want me to provide other definitions.

"You still have not answered the question about false but possible propositions."

The question at hand is, and has been from the original post by Rosa, "If God has always known what you will have for breakfast tomorrow, can you choose to have something else instead?" It has to do with knowledge (covered by Epistemology) and the actions of a person. We are dealing with actions and knowledge through time. If God has always known you're going to eat only Toast tomorrow morning then (supposedly) are going to eat Toast tomorrow morning. There is no other possible outcome in this world. In order to apply the "possible worlds" theoretical philosophy, you have to CHANGE what God has believed you were going to eat this entire time and THAT is where the time paradox comes from.

"It's useful to see that in order to stand by this faulty argument, you have to ditch an entire branch of modern logic."

Don't you see though that in order to stand with YOUR argument you have to ditch _every other_ branch of modern thought and logic? And even within the philosophical community this has been a controversy for hundreds, if not thousands, of years?

The deterministic world which is necessitated by an omniscient Christian God has long been understood and accepted to be contradictory to libertarian free will.

“Don't you see though that in order to stand with YOUR argument you have to ditch _every other_ branch of modern thought and logic?”

No, I don’t. Your impression to the contrary arises because, as you have now amply demonstrated, you don’t understand what modal logic is all about.

“And even within the philosophical community this has been a controversy for hundreds, if not thousands, of years?”

No. Certain issues—like quantifying into modal contexts, rendering of modal operators as adverbs, and iteration of modal operators—have been controversial in certain quarters (particularly, in Quine’s corner). None of these issues arises in this argument.

“The deterministic world which is necessitated by an omniscient Christian God has long been understood and accepted to be contradictory to libertarian free will.”

There are some Calvinists, like Jonathan Edwards, who will agree with this statement. But the majority of Christians who have thought about the matter disagree.

Sorry, but claiming there is no disagreement in the philosophical community about free will and determinism is just wrong or a willful attempt to move the goal posts.

"There are some Calvinists, like Jonathan Edwards, who will agree with this statement. But the majority of Christians who have thought about the matter disagree."

Thinking about it and disagreeing isn't much of an argument. They also have thought about evolution and disagree with it... but they're wrong there. They've thought about the earth being only 6000 years old... but they're wrong there. It's not a valid argument.

"Certain issues—like quantifying into modal contexts, rendering of modal operators as adverbs, and iteration of modal operators—have been controversial in certain quarters (particularly, in Quine’s corner). None of these issues arises in this argument."

You quoted only the final sentence of that and responded:

"Sorry, but claiming there is no disagreement in the philosophical community about free will and determinism is just wrong or a willful attempt to move the goal posts."

In other words, I clearly, explicitly indicated that I was talking about modal logic and whether, as you had tried to claim (after misunderstanding a comment in a Wikipedia article), it is "controversial" in some sense that matters to this argument.

In response, you started pretending that I was talking in that sentence about determinism and free will.

And then you complained that I was moving the goalposts.

Holy homunculus! That should win some kind of award for chutzpah.

I wrote:

"The charge is that the Christian conception of divine foreknowledge is incompatible with libertarian free will. Therefore, the Christian definition of foreknowledge and the libertarian definition of free will are the ones on the table."

In response, you tried to saddle the Christians with determinism, writing,

"The deterministic world which is necessitated by an omniscient Christian God has long been understood and accepted to be contradictory to libertarian free will."

I pointed out in my response that this is not the position of most thoughtful Christians, writing:

"There are some Calvinists, like Jonathan Edwards, who will agree with this statement. But the majority of Christians who have thought about the matter disagree."

And now you respond:

"Thinking about it and disagreeing isn't much of an argument."

Who said that it was an argument? We're talking about a definition here. Trying to win an argument by redefining the other person's terms and then insisting that he contradicts himself (according to your definitions) is intellectually sloppy.

The question has ALWAYS been about omniscience vs freewill. My point, which you clearly ignored or missed, is that the philosophical community has LONG considered this question to be a controversial one. Philosophers of all stripes disagree on the many points involved in it. However, you're claiming that it's all so simple and you've solved it with a simple Modal Logic "proof." It's not true. The paradox still exists, philosophers still disagree about it. The question has ALWAYS been about the contradiction between omniscience and freewill.

"Who said that it was an argument? We're talking about a definition here."

They are coupled. The widely accepted concept that a deterministic world eliminates the possibility of free will is the definition. When "thoughtful Christians disagree" it doesn't really matter if they disagree without a reason to do so. That's why it's not much of an argument when used to contradict my statement of its wide acceptance.

Then it was completely disingenuous of you to post that after quoting what I had said about a set of technical issues in modal logic as though you were correcting me.

As for the definition, most thoughtful Christians don't build determinism into the definition of divine foreknowledge. It's up to the critic to try, if he can, to show an inconsistency between an event's being foreknown and its being something done freely. You've tried, and failed, and been reduced to blustering about the supposed controversial nature of modal logic, which you obviously don't understand. The repeated bluffing and the rhetorical gamesmanship regarding topic shifting aren't doing much to establish your bona fides.

It must be a special feeling to be so sure that entire disciplines are full of morons, even when you keep being told that you're misrepresenting what they say every time you set fingers to keyboard. Imagine the fun a fundamentalist could have with that technique assailing evolution!

Fundie: "If biologists dispute that monkeys give birth to fully human children while simultaneously insisting that they do, then I think that says a lot about biology."

Biologist: "What? Who ever said a crazy thing like that?"

Fundie: "All I am doing is asking you to explain in simple English how these two mutually exclusive and contradictory ideas can both be true."

That might make sense, except that Compatibilism and Incompatibilism are two philosophical views which address the paradox of a deterministic universe and free-will. Compatiblists merely redefine "free will" in order to make it compatible with a deterministic universe (and therefore an omniscient God).

The non-Calvinists saw the contradictory position they were in and instead of changing their position, they just redefined the question to suit themselves. Much like in Rosa's new post entitled Bull's Eye.

I've answered every non-loaded question you've asked, and I've disambiguated more poorly formed questions than I care to go back and count. I think there may indeed be some amusement as people read this thread, but not in the direction you think.

"If God has always known what you will have for breakfast tomorrow, can you choose to have something else instead?"

If you can choose to have something else instead, but you NEVER do, is choosing something else truly possible (i.e., a probability larger than zero)?

For example: If I flip a coin, can it come up heads? Yes.What if I have flipped a coin 100 times and all 100 times it has come up tails? Can it still come up heads? Yes (too few trials).What if I flip the coin 1 million times and every single time it comes up tails? Can it still come up heads? Yes, although there now might be something fishy about this particular coin.If I want my coin flip to come up heads, but after an infinite number of coin flips it has come up tails every single time, then coming up heads was never truly possible. Just because the coin has two sides does not mean both sides are possible or probable.So, now on to the breakfast question: If everyone CAN choose a breakfast item tomorrow that is different from what god knows they will have, but in the history of existence they never HAVE and never WILL, then saying that they can is simply implying the illusion of choice without choice being an actuality. In other words, if after an infinite number of trials no one has and no one ever will choose something for breakfast different from what god knows they will choose (even though "they can"), then saying that "they can" is not actually true. Saying something is possible while simultaneously saying that its probability is equal to (and thus no greater than) zero is contradictory.

So it appears as though your answer to Rosa's question is actually "no," even though you say it is "yes."

First, your analysis, if correct, would apply only to repeatable events that are non-controversially in the same class, and that have their probabilities set by their membership in that class -- like coin flips. Individual decisions are another matter altogether.

Second, you write:

"If I want my coin flip to come up heads, but after an infinite number of coin flips it has come up tails every single time, . . ."

From an empiricist's perspective, it's difficult to make sense of its coming up an infinite number of times. Are you envisaging a situation in which neither you nor the coin ever wears out? How much time passes before you get the infinite number of flips? Worries along those lines pushed empiricists into the finite frequency camp.

". . . then coming up heads was never truly possible."

"Saying something is possible while simultaneously saying that its probability is equal to (and thus no greater than) zero is contradictory."

That simply doesn't follow; you're conflating a probability of 0 in real analysis with a logical impossibility. But any measure theory textbook will show you that there are non-empty sets that have zero measure on a given background set, such as the (infinite!) set of rational numbers in an interval on the real number line. If you want to assign non-zero values to those possibilia, you need to move into non-standard analysis where you can play with infinitesimals. Real analysis just doesn't have any other way to accommodate them than by assigning them measure (and thence probability) zero.

Your redefinition of "possible" is just that -- a redefinition. Like Humpty-Dumpty, you're free to use words that way. But it doesn't have much claim to capture normal usage, and it isn't a sense that most people working on this cluster of issues would recognize.

"First, your analysis, if correct, would apply only to repeatable events that are... in the same class, and that have their probabilities set by their membership in that class. Individual decisions are another matter altogether."

I can create the following set: All things (in the most general sense) that people can "do" that god doesn't know about. Granted, all of these "things" are independent of each other, but assuming god's omniscience to be true, this is the set of all things that god does NOT know people will do. It seems like you are arguing that this set is not empty.

"From an empiricist's perspective, it's difficult to make sense of its coming up an infinite number of times. Are you envisaging a situation in which neither you nor the coin ever wears out? How much time passes before you get the infinite number of flips?"

I tried to ease your difficulties by attempting to flip a coin an infinite number of times. My left shoulder gave out before the coin did. Never again will I use infinity in an example. The cost is simply too great.

When I referred to myself as an empiricist, it is quite clear that I did not fall within the bounds of your definition of that word. I'd hate to belong to a group that cannot discuss infinity without being expected to produce it. What I meant was that I wanted to assess the (potentially) observable occurrences of choosing a breakfast item different from what god knew someone would choose (can people AND will people?).

I have no issue with the argument that someone can choose something different from what god knew (i.e., this is a non-empty set). My issue arises when discussing will people choose something different from what god knows. From what I've read above, various people have stated that while people could have done so, they never have done so. If we just relied on observations, then I'm still on board; just because something has never occurred in the past does not mean that it cannot occur in the future. However, your point goes beyond that; Not only is it argued that no one ever has done so, but a statement is being made about all future occurrences of this event: No one ever will choose something for breakfast that is different from what god knows they will choose. The number of occurrences in the past = 0. The number of occurrences in the future = 0. It never has happened and it never will happen. How can one argue that "Event X has never happened in the past and will never happen in the future, but it can happen"?

Another reason that I chose to mention empiricism is because Rosa posed this question to theists, who (mostly) believe that god is (a) real and (b) omniscient. So, while these questions can be volleyed around among the different philosophies, Rosa's particular question should also be within the realm of reality for theists. With philosophy, infinity, and impossibilities aside: If part of a theist's reality is the belief that people never have and never will choose a breakfast item different from god's "known" choice (i.e., all past and future occurrences = 0), then how can she also believe that people can choose differently from what god knows they will choose?

Empirically, part of calculating probabilities is to assess the likelihood of a given event occurring in the future. If you are removing future unknowns by saying that Event X will never happen, then just because you say that Event X "can" happen doesn't make it so.

"But any measure textbook... such as the... set of rational numbers in an interval on the real number line."

These probabilities approach zero, but are not equal to zero.

"Your redefinition of "possible" is just that - a redefinition. Like Humpty-Dumpty, you're free to use words that way. But it doesn't have much claim to capture normal usage, and it isn't a sense that most people working on this cluster of issues would recognize."

Thanks for your permission. If you weren't so blatantly condescending, I'd swear that I sensed condescension in your response.

“I can create the following set: All things (in the most general sense) that people can ‘do’ that god doesn’t know about. Granted, all of these ‘things’ are independent of each other, but assuming god’s omniscience to be true, this is the set of all things that god does NOT know people will do. It seems like you are arguing that this set is not empty.”

This definition is ambiguous because “know about” is not well defined. There are lots of things that people can do that they will not do. God knows that they can do these things, and God knows that they will not.

“What I meant was that I wanted to assess the (potentially) observable occurrences of choosing a breakfast item different from what god knew someone would choose (can people AND will people?).”

Appealing to an infinitely repeated process is not, I think, a helpful way to model this situation. In any event, the events of probability 0 that occur in hypothetical scenarios of those sorts are infinitely long strings of particular results, not things like the outcome of some particular flip.

“However, your point goes beyond that; Not only is it argued that no one ever has done so, but a statement is being made about all future occurrences of this event: No one ever will choose something for breakfast that is different from what god knows they will choose. The number of occurrences in the past = 0. The number of occurrences in the future = 0. It never has happened and it never will happen. How can one argue that ‘Event X has never happened in the past and will never happen in the future, but it can happen’?”

Easily – by pointing out that the statement “X happens” is logically compatible with all relevant background information. This also answers your next question, how can a theist “also believe that people can choose differently from what god knows they will choose?”

“Empirically, part of calculating probabilities is to assess the likelihood of a given event occurring in the future. If you are removing future unknowns by saying that Event X will never happen, then just because you say that Event X ‘can’ happen doesn’t make it so.”

That is only one purpose of calculating probabilites.

I wrote:

But any measure theory textbook will show you that there are non-empty sets that have zero measure on a given background set, such as the (infinite!) set of rational numbers in an interval on the real number line. If you want to assign non-zero values to those possibilia, you need to move into non-standard analysis where you can play with infinitesimals. Real analysis just doesn’t have any other way to accommodate them than by assigning them measure (and thence probability) zero.

You reply: “These probabilities approach zero, but are not equal to zero.”

This is not true. Please consult a textbook on measure theory.

I’m sorry if you found my remarks about your redefinition of terms condescending, but when you enter an ongoing conversation that has stretched across centuries and immediately insist on imposing definitions quite different from those that almost everyone else is working with, you bear a significant burden of showing why yours should be adopted. As Rosa’s own ground rules state: “Whilst you are entitled to your opinion, you are not entitled to have it regarded as established fact needing no supporting evidence or justification. Don’t be surprised if you are called on an unsubstantiated claim.”

"This definition is ambiguous because “know about” is not well defined. There are lots of things that people can do that they will not do. God knows that they can do these things, and God knows that they will not."

This is no fault of my own. God's omniscience is itself ambiguous and ill-defined. The set "Everything god knows about" should then be equally ambiguous.

"These probabilities approach zero, but are not equal to zero.”

"This is not true. Please consult a textbook on measure theory."

Thanks for the guidance. According to my understanding, the probabilities of examples such as the one you provided are said to be equal to zero to give them a "workable" value. In other words, because they are small to the point of being essentially zero, they are said to be zero for the sake of practicality. To use a different example: when conducting a significance test, if the p-value comes up as "p = .000," we do not say that p = .000. Instead, we say that p < .001; just because the probability reported is said to be zero does not mean that we can ever say that the probability is actually zero. My point is that, depending on the discipline, values that are essentially zero are (a) sometimes said to be equal to zero and (b) other times said to be almost zero, depending on their use or purpose.

"I’m sorry if you found my remarks about your redefinition of terms condescending..."

Somehow, I don't think you are.

"but when you enter an ongoing conversation that has stretched across centuries and immediately insist on imposing definitions quite different from those that almost everyone else is working with..."

Let's not generalize so grossly. My jumping into the conversation with a different perspective from yours is very different from "immediately insisting on imposing definitions quite different...". I think this also suggests that you've assumed that I hold fast to the "definitions" I "insisted" upon.

"you bear a significant burden of showing why yours should be adopted. As Rosa’s own ground rules state: “Whilst you are entitled to your opinion, you are not entitled to have it regarded as established fact needing no supporting evidence or justification. Don’t be surprised if you are called on an unsubstantiated claim.”

Thanks again. Restating Rosa's ground rules has allowed me a whole new understanding of their intent.

First, there is no "begging" for forgivness which implies we must earn it. No, instead it is a gift. Freely given by God through the death, burial and ressurection of Jesus Christ. It is by grace. Please study up on the meaning of grace. Secondly, I look at all you have posed here in another light. God IS all knowing, yes. God gave us free will, again, yes. Try to look at it from this view if you will. Everything created on this earth was for us. A living earth to sustain life, for us. By studying the word of God, it all points to His plan and purpose. He could have chosen to make us perfect and worship Him, but then we could be considered nothing more than drones. Instead, this was the best way, not by human standards because we are fallable creatures, but by Gods standard. The best way for Him to reveal Himself to His creation, those who love Him. Let me ask you this. If you loved someone so much, what lengths would you go to make them love you back? If you had a love potion would you cast a spell on them in order to make them love you?? No. You would know it was true if they loved you back on their own free will. God wants a relationship with His creation but He wants us to love Him back by free will. Yes He knows what we will choose to eat. But that is irrelevant. He is interested in our hearts. We have choices to make daily, just because He already knows the outcome, doesnt mean we cease to live. WE as humans dont know what will happen in the next minute, much less the rest of our lives. Just for the record, your questions do not make me squirm. I welcome them because it means you are seeking. If you werent, you wouldnt ask. I welcome your messages out of love. You are human just like me and when all differences are put aside, you need love just as much as the next person. Hope you have a wonderful day Rosa. My answer here was not meant argumentively, only a thought to ponder if you will.

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